Yes. I got a semi-legit birth island shiny mew after about a month of SRing, but at that time I didn't know about the RNG thing. It's not impossible to find shinies on emerald, most of the people I know have found at least 3 on emerald.
It never took me more than 30000 SRs to get a shiny (thankfully), but my longest hunts were rayquaza (about 25000 srs) and zapdos (about 20000 I think). Any other shiny that I SRed for didn't take more than 15000 srs. My shortest hunt was shiny moltres, only 42 srs :O. Wow.
Drifloon hasn't shone yet. But I'm taking a small break to try my luck at chaining in the sandstorm. Nothing great, so far