With flash your shutter speed would be limited to 200 or 250 which is not enough to freeze motion
Sorry, but this isn't accurate (no disrespect intended). When artificial light is used properly, the duration of the flash/strobe is what freezes the action, NOT the shutter speed. All the shutter speed does is control the exposure for ambient light. Lots and lots of information on this and other forums about using flash for indoor sports (including the third episode of the podcast in my signature).
Having said that, if the gym in which you are shooting is anything like the hundred or so I've worked (even with new lighting), an f/4.0 lens of any kind isn't going to be good enough to get much more than 1/200s -1/320s with your 300D's limit of ISO 1600. So, you're left with the option you are considering: flash or lower aperture.
I am a big fan of artificial light when working indoor sports, however I am not a big fan of on-camera flash. Again, take a look at the podcast mentioned above.
The 85 f/1.8 is a cool lens for many things, not the least of which is basketball. I personally think it's a little short, and that shooting it at f/1.8 yields a really, really tiny depth of field. Every once in a while I'll drag mine out and use it for hoops, but inevitably I put it back in the bag and replace it with the 70-200 f/2.8 for the reach and quicker AF. YMMV, though.
Hope this helps.