Gents,
Didn't drain the oil before removal of engine, and now I'm thinking of just replacing the oil cooler seals while I have it out. If I remove the oil cooler from the engine to clean it and whatnot, am I going to get oil everywhere?

You can tell I'm not familiar with how the oil flows, so I'm not sure if I remove the cooler if oil will start gushing out of somewhere

Thanks! Going to try to tackle this job today!

I think you'll find that oil obeys the law of gravity...
There will be some trapped in the cooler but mostly it drains out.
Keep the engine right-side-up and it won't be horrible.
However, when dealing with oil-filled receptacles, it's always best to expect them to drip (although not gush, exactly). Have power towels and shop cloths at the ready...

I would say no as long as the engine is kept "level". The level of the oil in the sump is below the oil cooler seal line. You have to take the fan husing off to REMOVE the oil cooler but it's possible to replace the seals without removing the cooler. But you can replace the seals with the engine in the car. If you're removing the engine for something else, why not drain the oil; only at most 4 qts.