There is a good chance that it won't receive updates. Normally it got OTA updates through Bell. Telus does have the same model of phone but it's not certain it'll be able to use the OTA updates from Telus.
I suspect that the phone will continue to get OTA updates from Bell. The updater needs access to the Bell servers from any connection on the Internet for Bell customers. It wouldn't make sense to only allow connections from the Bell network as most people update over WiFi which could be any ISP.
The only hitch might be if the updater checks for a Bell SIM card before it updates but that really doesn't make much sense either.
Check for updates once on TELUS and see whether you get an error or the normal "Your system is up to date" message.