A shaving brush is really designed to be used with traditional shaving soaps or creams. Shaving gels are not intended to be used in this manner, so short answer, 'no' (some such products may even contain ingredients that will damage a brush's hair). Decent soaps or creams however, can be had fairly inexpensively. There's a technique to making your own lather, but it is not so difficult.
Some people create lather in a bowl (suitably sized / shaped ones can be bought cheaply. I got mine from Sainsbury's), others in their palm, others still 'face lather'. Youhave to experiment, see what works for you.
Edit. : Check out Mantic59's videos on YouTube for all things related to traditional shaving. He has some great advice for novices and old-hands alike.