Verizon Windows phones will work out of the box with GSM networks, so long as the bands support it. T-Mobile tends to have a problem sending text and mms over 4g/3g networks (works over 2g for some reason), but generally I didn't really run into problems with my 928 on AT&T. The one issue I have had is with trying to use Verizon's LTE after setting APN settings in Access Point. Basically, Verizon doesn't have any APN settings with Access Point because the SIM takes care of configuration, so without APN settings to set, it keeps using the AT&T or T-Mobile settings. The only way to get LTE working again is with a full reset if the phone.
Edit: for full disclosure I have not tried a T-Mobile SIM in my Lumia Icon yet because I don't want to have to reset it to get Verizon LTE back, my experience is based on my Lumia 928 on the Amber/GDR2 rom. The Icon should be the same
Finally: dont verizon phones usually need a verizon sim at their first boot up to be "registered"
I haven't had that experience with Windows Phones, only Android Verizon phones (HTC One in particular). I think Windows Phones work more like iPhones in this regard.