Can I Have a Blepharoplasty if There is Still Some Filler Left?

You have found out that fillers are no good for the lower lids. I also recommend fat removal instead of repositioning.  Repositioning of the fat sounds like a good idea, but in reality, it really doesn't do what you think it will and you will return later to simply gave the fat removed.  Keep it simple!

Hyaluronic acid can be dissolved with an injectable enzyme, so it is possible to remove the product before undergoing blepharoplasty. That way, it will be clear to see what microsculpting of fat needs to be done.

It is possible to have eyelid surgery in the presence of lower eyelid filler. However, your first job is really to find the right surgeon. That person should have solid training and reputation. However, you need to study their before and after photos as well.
If there are things in their work you do not like, don't assume because the surgeon is charming or that the are reputed to be "the best," your work will be any better that what you see in the before and after pictures. Remember, the surgeon presents these pictures not as representative of their work but because they represent the absolute best of their work. The right eyelid surgey will assess you and determine the best approach for your particular situation.