Well I already did the gig before I started this thread, so I got through it OK. I don't know if all the songs were from the Real Book or not, but there might be more gigs with this lineup in the future and I'm thinking I should get this book, any help I could get would be worth it.
I've gigged as much on bass and keyboards as I have on drums, and I've done not only a lot of jazz gigs, but a LOT of "society" gigs--those are Real Book central. On most gigs I've done recently, Real Book II tunes tend to be used at least 25-30% of the time, so you should know tunes from both. I haven't run into many people who call tunes from Real Book III yet, as too many cats don't have it--including me.
As a drummer, I don't think it's necessary for you to actually BUY a Real Book. What would be far more invaluable is to go through the table of contents of at least the first two books (you can find this here:
http://www.hickeys.com/pages/realbook.htm) and if you do not mind downloading stuff at least for research purposes, download multiple versions of each one of those tunes--look for jazz artists you recognize if you can find them--put them on your MP3 player (or just use your computer), and listen to them over and over until you get to know the tunes. It's important that you check out at least a few versions of each, as there are so many different ways to approach them. If you're adamantly against downloading anything, you can find versions of most of those tunes on youtube, but it's better if you can listen to the music while you're doing other things--at a day job in headphones, walking, in your car, etc.
Without having the Real Book, and until you learn the tunes, you're not going to immediately know the style of the tune or the rhythm of the melody in the head, but lots of guys call out the tunes in different styles anyway ("'Giant Steps' as a samba" for example), lots of guys play the heads a bit differently anyway, and I've never met a bandleader who would think it's out of line to call out the style after he calls out the tune anyway. A lot of guys don't know all the tunes in the book even if they have the book, and some of the tunes with more unusual structures, like Pat Metheny's "Unquity Road" (I think misprinted as "Uniquity Road" in most Real Books), are not going to be called by a bandleader if some of the players on the gig are unfamiliar with them--there is just not enough information in the Real Book for the tune to work well if you don't already know what it sounds like. (By the way, re "'Giant Steps' as a samba"; it's important to at least know the basic Latin grooves--what differentiates a samba from a rhumba, bossa, etc.)
The other advantage of downloading and studying the tunes is that you get to hear a lot of great drummers already playing those songs. You can steal a lot of those ideas, and if you do something on a Real Book gig just like Elvin Jones, say--or at least referencing something like that, and you're playing with real, knowledgeable jazz players, that will put you in their good graces even more and probably lead to more gigs.