Engine Flushing Through Sea Strainer

Do you mean that your yard stored the boat without flushing the engines and filling them with antifreeze first?
You'd better move the boat elsewhere, methink.
Anyhow, the answer to your question is no.

Pump cavitation is never going to happen if the water from the connected hose is pressurized, which of course it would be.

And it's pointless to compare the strainer size with the garden hose, because the former is designed for the maximum flow at 2300 rpm, while the latter must only cope with the demand at the idle speed of 650 rpm.
Now, that looks like a 3" strainer with a 3/4" hose tail on the lid. And if so, I can confirm that the flow is sufficient for feeding the MAN V10 running at idle, of course assuming a good incoming flow from the connected hose.
On the other hand, if that's only a standard 1/2" hose tail instead, I'd rather go larger.
Actually, I'd rather do something different anyhow, fitting a valve upstream of the hose tail, for rather obvious practical reasons.

Regardless, that's not what the OP asked, because he wants to "run fresh water directly in the strainer without cracking the engine", whereas by cracking he meant cranking, I suppose.
In other words, he was thinking to flush the engine just by forcing fresh water through the hose tail, which is the reason why my first short answer to him was no.
If you don't mind cranking the engine and keep it running at idle for a while (and I don't see why it should be a problem, unless forbidden by some yard where the boat is stored inside), what I explained in this post is imho the most practical way to skin this particular cat.

Positively +1 to what Oscarvan said, also because it doesn't depend only on the engine.
Also how a wet exhaust and its raw water re-injection (or shower heads, as Oscarvan called them) is built affects the risk of water reversal into the turbo, possibly down inside some cylinder, with potentially catastrophic consequences.
Ideally, you would want to talk not only with someone who knows your engines like the back of his hand, but also your exhaust system - which depends more on each boatbuilder, rather than engine manufacturer.
Though a good mechanic should be able to evaluate and asses the inherent risk of any exhaust system after a careful inspection.

I'm a fan of engine flushing in general, but without knowing for sure that there's no risk of water reversal, Fiammetta's suggestion does make sense.
Unless the boat is in an environment subject to freezing, of course.
Engines neither like water in some cylinders, nor ice expanding inside them.
You don't want to jump out of the frying pan into the fire!

Hindsight is a great thing, but the OP boat is already on the hard, stored in a place where turning the engines on is forbidden...

The risk you describe does exist, but it's very easy to avoid it.
After you open the fresh water valve on the hose attached to the strainer, and you close the raw water seacock, if the engine pump demands more water than the hose can supply, you will immediately notice that the rubber hose gets squeezed, due to suction from the engine pump.
And of course, if that happens, the flush must be postponed till a decent fresh water flow is available.

For this purpose, below is a photo of one trick which I didn't mention in the thread that I linked at the end of my previous post #5:
a simple "Y" split hose, that allows to connect the (white) engine flush hose to two taps in parallel, granting a higher flow.
I normally don't need it in my home marina, but it came in handy in some others.

Yep, moot point.
But just for the records, you can trust me if I tell you that there's not a snowball chance in hell to starve the engine of raw water, if you know what you are doing. Been there, done that, many times.
It's actually easier done than said, but whenever in doubt about how adequate the fresh water flow is, I do as follows:
Firstly, I turn on the engine and keep it idling, with the fresh water hose already attached but its valve closed.
Then, I open the fresh water valve completely, and start closing the seacock slowly.
Now, if the fresh water flow is good enough, the hose will not collapse, and the strainer will stay full, till the seacock will be fully closed.
At that point, you can keep flushing the engine for as long as you wish.
But if while closing the seacock you'll see that the hose starts collapsing, and/or you see any void in the strainer, you can simply re-open the seacock right away, and postpone the flush.
It only takes half a minute of attention, really - much less than it took me now to write about it!

In the swamp. more hoses in the open strainer works better. Required during red-neck Dyno runs, dock side.
Usually not enough lines holding the boat in place vs water hoses going to the open lid strainer.
Here, hold my beer,,,,,

I will tell you, one hose will keep the impeller wet and push enough water thru the engine to keep it cool at idle, even if the hose looks thin, it is delivering water.
If your looking for a good flush, more hoses at the strainer will work better. 5/8-3/4" hoses will only flow so much under any city water pressure. It's volume that will keep the strainer full and hoses from sucking thin.

When we dyno'd rebuilt engines in my shop, had a tower tank outside to ensure lots of clean raw water to any engines built.
Here is when I learned about thin hose sucking down at high RPM.
Since then, only wire reinforced hose on the low side of any pump on our boats.

Yeah, the above setup is strictly meant for flushing an engine at idle, that's a given.
I do understand that an engine with a 3" strainer can't be ran at WOT feeding it with a 3/4" hose!