Can a wifi transmitter generate RF of different frequencies?
Although the components inside a WiFi AP (access point) may be able, if programmed appropriately, to be able to generate other frequencies, that interface is not available to a user of the AP, there just are no software 'knobs to twiddle' when connecting to it.

If you pull one apart physically and poke at the board, or hack it down to the firmware, then you may be able to coax other frequencies out of the components. You may rest assured that as the hardware has only been designed to handle the correct WiFi frequencies, any filters or line lengths in the AP may well be wrong for those other frequencies.

Now if you buy a 'software defined radio' (SDR), you'll find many of the same components in it that you'd find in an AP. The difference is that it's been designed to let you fiddle with it, it actually presents a programming interface to generate and receive different frequencies, and has a more general purpose RF path design.