I got curious about this comment and it turns out they've basically never actually drafted a useful QB in the regular draft, in any round. Kosar was a supplemental pick and Otto Graham was pre-draft era. They drafted Brian Sipe in the 13th round and he started for several years for them. That's the closest/best I could come up with.
I think Cleveland did themselves a favor by not drafting one of those two pretender 1st rd QBs this year - part of the reason none of the other QBs they've drafted have worked out (besides from they all suck) has been a lack of sufficient quality around them in both talent and coaching. They need players in volume, and it looked like that's what they were trying to do. I am interested to see how their 'moneyball' front office experiment works out. Of course with their history, it's possible both Goff and Wentz will be monsters as the next-gen at QB and the Browns be ridiculed for decades for trading out of the top of the draft. Or maybe Lebron bringing the NBA title back will signal the new era of Cleveland sports dominance. They've paid their 20 years penance for moving the Browns and firing BB. RGIII is exactly the kind of reclamation project I could see working out well for them (not MVP level, building block/ quality veteran level).