Just realized you might be starting with just the 2" squares and be cutting different sized strips -- yes, you can still use those in the center even with a different sized log. Usually the center most log is the same size or larger than the logs around it, but it doesn't have to be. Can be smaller too. It will still end up square.
The only problem I can foresee is that your blocks won't match your ruler -- but people were making log cabin blocks for a long time without much in terms of a ruler at all.