Yes, many people did that!

The BCIS rule is you can renew TN while Labor Certificate and/or I-140 are pending/approved. But you can't do that once filed I-485.

So file LC first, once approved you have two options:

1. Renew TN, so you have one year in hand and file
I-140+I-485+AP+EAD concurrently. 180 days later, you will get AP+EAD in hand so that you will never need to renew TN anymore.

2. File I-140 seperately and once approved, instead of file I-485, apply immigration visa from Montreal consulate. This is a fast way due to immigration visa usually takes less time that I-485. You can still renew TN each year before immigration visa issued because you have clearly show your intent is to back Canada to finish immigration processing so that the current trip on TN (renewal) is to perform short and temporary professional services. That means you can renew TN without immigraiton intent barrier.

The above explanations are from BCIS. In past, more than 70% Canadians got their GC through this process, especially white guys.