Ok, I'm a bit late to the party but I have a couple of questions.
How is the engine mounted in the car? Does it still use the factory front mounts and a rear mount on the trans or did who ever put the 327 in it install side mounts on the engine? Also were all of the bell housing bolts in place and were they tight?
It's been common knowledge for a lot of years that a Tri 5 Chevy running a V8 with front mounts and an aluminum case transmission can flex at the Block/bellhousing connection enough to crack the trans case or cause problems with the flex plate. I've also seen a couple of cases where loose bellhousing bolts caused a broken flex plate or knocked out the front seal in the transmission.
I'd do as a couple of the guys suggested and put a new flex plate on it and pull the plugs and run a compression test. You can see if the engine has oil pressure at the same time by connecting a gauge to the engine where the oil pressure line or gauge hooks up. Using a oil pump primer as was suggested earlier would be a good idea though as it gets oil up in the lifters and into the bearings.
You don't need a fancy stand and can hang the engine from a chain hoist or cherry picker to run the compression test as all you are doing is cranking the engine over so that each cylinder hits four or five times on the gauge, checking the reading and writing it down and going to the next cylinder. I've even started a lot of engines sitting on the ground or hanging from a chain hoist.
This is a short video from when I fired up a 500 Cad that my friend gave me for my 71 GMC the engine had been sitting for several years.
I couldn't run it more than about 30 seconds but I did find out that it ran ok. No engine stand or other equipment but as I said I only ran it long enough to hear it run and determine that it didn't knock or blow clouds of smoke.
As far as the 327 goes, if it is in good shape I'd either run it as is or rebuild it and put some better heads on it. 1. it gives the car a lot higher Bubba Factor with a 327 than a crate motor these days as a lot of guys still think a 327 is the Holey Grail of small block Chevy engines. 2. you already have it and can go several ways on it. You could run it as is if it checks out. You could do a complete rebuild with new pistons, new cam bearing, better cam and better heads or you could do a rering and bearing job and run the pistons you have if the cylinder bores are good with little taper.
If the insides of the engine don't look good then you can think about a different engine and think crate motor or rebuilt.