Yes, so long as the HDD was originally formatted by the same PS3, it should boot up just fine and not ask you to format it.
The way that the PS3s format their HDDs puts a unique identifier for that console on the HDD. So you can't take a hard drive out of one PS3 and place it in another, but you can apparently swap them in and out of a single PS3 with no problem.
In fact, Sony would request that you put back the original HDD for warranty repair:
- What to do with that leftover drive? Put it in the anti-static bag that you got with your new internal HDD. You need to hold onto it, because if you need to send your PS3 to Sony for repair, they will ask you to put the old HDD back in.
Here is a user who was in a similar predicament to you, and apparently was able to swap it back in no problems.
See @djsmiley2k's answer which covers the options you'll need to set when swapping the hard drives back.