Water can run but it is a waste of water.
If you have a crack in the cylinder wall like mine had, it would only suck in water under pressure when the water pump starts circulating the water around the block.
Of course you need your engine running for that.
Check around the block and see if any freezer plugs popped out of place or look like out of alignment or use temporary rubber plugs or look way too new compare to others.
If you can, get a scope inside the cylinders by removing the spark plugs, I could see a lot of rust in one of my cylinders that had walls cracked around it.
You can also take out plugs one at a time and try to start or even let run if it does, and see if any start spaying water out or are just wet and rusted compare to others.
There is a slim chance that your manifolds might be leaking.... but small. Probably just a bad block.
You said that you just got this engine, was it used or "brand new" remanufactured block?
I'd stay away from used as you never know what kinda crap people want to unload.
A new reman long block is guaranteed and not that expensive and does not add many hours to the swap compare to the troubles of the bad used engine.
You can also have bad head gasket that would let water in when the engine is running.