This is all In My Humble Opinion ...

I can liken this to a car.

Your guitar (and its pickups) are like the type of gas you can put into your car. Low octain, high octain or even mixed with a little NOS - all can have an affect on how your car runs.

BUT ... ...

Putting high octane mixed w/ NOS in a '97 Geo Metro won't be quite the same as in a '69 Camaro.

Your amp is like your car engine, and your effects are all the extra little tweaks that make it sound (or look) extra cool.

So to answer your question -

The type of guitar you have CAN make a difference IF you have a high quality amp and effects to drive.

If your amp is low or mid quality, the type of guitar you have is less of an impact. I'd go with what tehplatypus recommended.