That is very unlikely. Crashing would happen 100% of the time though. Most people want that trade-off (meaning: If their browser would crash, they would switch to another one, even it was less secure).
Corrupting SP is part of almost every exploit and I can guarantee you that it is very likely (going to cause harm on your system).
Try to pull Metasploit GIT repo to get some idea about thousands of payloads that do corrupt SP without crashing the host...
Yes, but how many of all cases of corrupted stack pointers are exploits?
Why would that matter? We're not trying to be secure against random cosmic rays. We're trying to be secure against attackers.