There are a number of places that colocate normal Raspberry Pi.

https://lowendbox.com/blog/little-machines-in-big-datacenter...

I am sure that some of them either already colocate Pico ones too, or are willing to do so if asked.

The Pi Pico doesn't have networking capabilities, so that would be silly. You're probably thinking of the Pi Zero.

There is a Pico W