martinibuster - 3:15 pm on May 23, 2013 (gmt 0)
I can't answer your question from personal experience. However in my opinion it's possible your rankings may be supported by other factors. Here is why I think so:
1. "Powered by" links have been targeted for depreciation for almost ten years. They have steadily been losing efficacy (for the purposes of ranking) ever since.
2. The location of the link within the web pages might be cause for a depreciation of the usefulness of the link for ranking purposes.
3. The fact that the link is run of site does not make it more powerful either. So the usefulness of the link may have been overstated to begin with.
4. Words such as "powered by" could be cause for diminution of usefulness of the links for ranking purposes.
All of the above are reasons to be suspect about the usefulness of the links. Let us know if the removal of those links does indeed cause a change in ranking. It's possible there won't be much of a change.