If you are planning on getting a phone from overseas, you should ensure the phone has the proper compatible bands/frequencies. You can verify those bands/frequencies here. It should also be noted that Rogers plans to decommision the GSM network by December 31, 2020 (see here).
A phone does not need to have all of the compatible bands/frequencies to work on the networks. However, coverage depends on corresponding bands/frequencies available at your surrounding cellular towers. Not all bands/frequencies are used at all cellular towers. You can get an idea of your surrounding cellular towers here.
In addition, it should be noted that the different bands/frequencies have varying characteristics. For example, the higher frequencies generally have a greater potential bandwidth than the lower frequencies (see table here). On the other hand, the higher frequencies tend to decay faster. That is, they do not travel as far, nor penetrate as well as the lower frequencies (see graphic here).
Hope this helps