Yes, Pik TV will work on non-TELUS internet, including Wi-Fi and LTE.
A few things to note, however:
Pik TV is only available for TELUS internet customers, so you can watch it on a different internet connection, but you must be a TELUS internet subscriber.
Due to some content-provider restrictions, a few channels will be unavailable outside of your TELUS home internet. Currently, 92% of the channels available on Pik TV, including all major Canadian networks, all sports channels and 82/85 choices in the Pik 5 are available out-of-home. If there's a specific channel you're interested in, feel free to reply and ask, otherwise there are details at https://www.telus.com/tv/pik/channels (click on an individual channel logo and look for 'watch on the go').
Streaming Pik TV away from your TELUS home internet will consume internet or cellular data.