The math should show the truth!
Lets say the average size of a piece of spam is 30KB (a bit high, I know) and figure the current 2696 MB mail box at Gmail and that the Gmail Spam Filter will catch 90% of your spam (which is on the low side IMHO) and that the spam box clears itself after 30 days.
You would need to get more than 90,000 spam emails in the first month, 81,000 the second month (that 10% sitting in your inbox), 72,000 the third month, etc.
I would say it is safe to say you won't get 90,000 pieces of spam. So while you could get a lot of it, it would take years before the mailbox is full. Any by then Gmail will probably be an unlimited email account.