Yes, your C64 will work with a 60Hz mains, but programs may behave differently.
The 9VAC supply is indeed used as a timebase. This is the part of the circuit that does the job:
As you can see, it is used to clock the TOD (Time Of Day) realtime clock inside both CIAs (CIA2 depicted here). The CIA can be clocked with 50 or 60Hz and it has a bit inside a register (bit 7 of CONTROL TIMER A) to tell it whether the input frequency is set to 50 or 60Hz. This is used to keep some counters that track tenths of a second, seconds, minutes and hours.
It is the ROM which is different for PAL and NTSC systems, which actually set or reset this bit accordingly. C64s with a PAL ROM will set this bit. NTSC ROMs will reset it.
If you plug your PAL-aware C64 into a 60Hz mains, you will notice that applications that use the realtime clock will show the wrong time, updating it too fast. So any application that uses this to time events will trigger them at wrong intervals, which may or may not be problematic.
This timer is not the same as the VBlank. VBlank will keep updating at the vertical sync frequency your VIC-II is designed for (that is, 50Hz PAL in your system) so I expect games and demos won't tell any difference.
According to C64-Wiki, the TIME system variable doesn't depend on this TOD (???)
There is a great article at CODEBASE 64 which explains how you can figure out if your TOD is running at 50 or 60Hz, and configure it the right way.