Yes.

I know someone from China with only a bachelor degree who held an H1 visa when entering U.S. He said it would be really hard for him to get American GC so he applied for Canadian GC several months after his arrival. Then he got it approved. He is in IT field. When he got lay off, he went to Canada and found a job there.

A friend of mine immigrated to Canada first, then became Canadian citizen. Then came to U.S. She applied for American GC just like us. Now she is holding both American GC and Canadian passport.

If you are sure you can get GC here, don't have to consider the Canadian GC. It will be really hard to maintain both GC valid.