Does the 4 GB Xbox 360 have enough space for 5 gamer profiles and saved games?

Yes, that should have more than enough space for that. I've had my Xbox 360 for close to two and a half years, and after playing 100 or so games my profile takes up about 10MB. As for save games, I'm not sure how much space mine are taking but most save games are less than 1MB so there should be plenty of room for them as well.

If you do need more room and don't want to spring for the 250GB hard drive (now or later - it is cheaper to buy it with the console, though) you can always use USB drives for storage. The Xbox 360 supports drives up to 16GB.

Note that the vast majority of games don't require a hard drive, but some do. The only ones I'm aware of off hand are Halo 3, Halo 3 ODST, and Halo Reach. In this case, you can play the game but you can't play the campaign or Firefight in co-op mode (at least online - not sure if the same restriction exists for local co-op).

It has enough for a saved games, but a concern would be that it restricts you ability to download updates and DLC for games, which can interfere with your ability to play online. For example, Burnout Paradise's free updates along would use up 1/3 of your space. And while Burnout is an outlier in file size, it's still possible for free updates of an average number of games to fill that drive. On my 360, which I've had for a couple of years now, I have 9GB used up between DLC, updates, saved games and three albums.