Unlocked phones are not carrier-locked, they'll work on any network, including Public Mobile (Telus).
Pretty much any phone meant for sale in Canada (or USA) over the last half decade is assured compatibility any of the major Canadian cellular networks. Phones using legacy radio or phones intended for foreign regions/markets typically won't work (although "global" phones often support CA/US). All compatible phones will support basic talk/text/data/etc, but not all compatible phones support all the latest-generation protocols and bands and frequencies and features, but this isn't an issue on Public Mobile (which throttles LTE data to "3G Speed" and which doesn't support stuff like VoLTE, etc).
Whether or not the phone is paid for isn't relevant. Unless the previous owner has secured or locked it in some way which prevents or limits usefulness to the current owner. Yes, they could get the phone blacklisted (registered as lost/stolen/etc) which would basically make the phone a worthless brick. Or they have installed modded firmware/software of the variety you don't want.
Buyer beware. If it's an option, plug your SIM card into the new/used Pixel to confirm compatibility before walking away from the deal. And (if you're unafraid of voiding the warranty which doesn't apply to you) then consider installing a clean copy of GrapheneOS.
