You will not. Nevertheless, understand that when you buy a used Mac without the disks you run the risk of buying a stolen computer. He should have given you the password for the computer--not "create an Administrator account for me."
Why would he not give you that password; it is not his computer anymore?
The answer to your question is "no" if the disk is a "grey" disk and it is not from the same model. You are free to try it, of course. If that does not work, your only options are to purchase a retail disk, hunt down your "friend" and force him to cough up the disks that came with the computer--I find a cattle-prod most efficacious--or perhaps get really, really lucky getting one from Apple or an on-line dealer. That is the "grey disk." Retail disks for OS X are easy to find, particularly for the lower OS like 10.4 which is a fine and wonderful thing.
That is the bad news.
The good news is that you will not have a paperweight. At worse, you can clone the drive . . . wipe it . . . install a System . . . set it properly . . . then pull over your data. Do not merely "transfer accounts"--you may recreate the same problem.
At best, with a proper OS disk, you may be able to change the passwords, remove superfluous accounts, et cetera. There are threads on how to do that on this site--it is pretty easy.
Regarding drivers, if you have "third-party" things like a printer, those should come with the printer, obviously, or most companies now have them on line or will get them for you. In fact, many Mac users "save space" not loading all of the printer drivers available. They can always get them later, and they are often updated.
Regarding your airport card, it depends on the maker. If it is Apple--no problemo. Third party should have drivers available on their Web pages. I had one for my Widdle Old Pismo, and their maker not only had that but the instructions on how to make sure the Mac recognized it.
--J.D.