Does powering a module with 5v instead of 3.3v affect it's logic level?
With no datasheet, it's difficult to say. Generally speaking, V In High max will be VCC + 0.6 maximum. And V Out High will be at least VCC * 0.7 to max VCC. This is true 90% of the time.

But you never know of the IC has multiple internal voltage levels. Some ICS may have 5V VCC, which it regulates internally to 3.3 and 1.8, and logic will be tied to the 3.3v. 

And that module has a sot-23-5 IC, which may be a voltage regulator. So while the module is 5V in, the actual IC runs on 3.3v. 

So datasheet is important here.

Update: The IC's data sheet confirms what I said above. Max 3.6V VCC for that specific GPS IC. The 5 pin sot-23-5 is likely the mic5218-3.3 3.3V low dropout linear regulator. No 5V tolerance at all on the data pins.