Drums are a very... different instrument from the sax. If you're given the opportunity to try before setting down to try it, I suggest doing that. It'll be a huge change, and yeah, they are very, very loud. You'll be stuffing your drums within a week of buying them, I'd bet.
In relation to your brother, you could totally accompany his guitar with the saxophone anyway. Most teachers move their students into jazz and blues within a relatively short time, and until then, you can rock out on the saxophone to whatever he's playing, no problem. There have been a fairly large number of rock songs that have featured the saxophone. For instance, this highly famous tune with a gorgeous sax solo:
https://www.youtube.com/watch?v=9UzBSxoXVRs
You could really easily play around with it to give the sax more playtime, too.
Or, how about the Boss? Jungleland has a great sax solo, as well!
http://www.youtube.com/watch?v=JR_0nbEzVdY
And then, of course, there's this:
https://www.youtube.com/watch?v=3khH9ih2XJg
How can anyone ever forget Bob Seger's Turn the Page? It's a pretty easy song to play on guitar, and it sounds great.
Another option, he's pretty much guaranteed to learn "Mr. Bojangles", I've yet to meet a guitar teacher who doesn't teach his students that song, and you could play King Curtis' version, which is entirely saxophone, to his guitar.
https://www.youtube.com/watch?v=DGcZ37--BXM
These are just suggestions for the saxophone. There are a thousand things you could do, including learn the drums, but if you go that route, I seriously recommend trying it before buying it, so to speak.
Here are a few other suggestions for new instruments, if you decide the drums just aren't for you:
Guitar (I know, your brother plays, but it truly is an amazing instrument. I've been playing for years)
Bass (More or less the same, thicker stringers, wider frets, longer fretboard, of course, and less strings. I've been playing this longer than guitar)
Banjo (Easier tuning than the guitar, different sound, but you can jam)
Piano (The piano is fun. It's not hard to play, once you figure out where the notes are, and it's an instrument that never needs anyone else for it to shine - like the sax. I've dabbled for a few years, myself.)
Trumpet (This is another fun instrument. Great for a whole plethora of genres, but you might be able to talk your brother into doing some ska-punk, like Goldfinger or Reel Big Fish.)
Trombone (See: Trumpet)
Harmonica (A very... unpopular instrument, although I've never understood why. The harmonica has a somber sound, which is why it's so good for blues and country, but it can also be really upbeat and fun(see: Free Willy), hence its use in bluegrass, as well. I've been playing around with these since I was a kid.)
Tin Whistle (These are one of my favourite instruments. They're simple, yet elegant, and so much fun. Great for all kinds of folk.)
Pan flute (On that note, the pan flute is a ridiculously beautiful-sounding instrument, haunting and hollow and just fantastic. Plus, it has a really cool, exotic sound to it)
Violin/Fiddle (I'm partial to the fiddle myself. Toe-tapping, intricate and delicate, perfect for Western-European folk styles, especially Celtic)