Can I file a complaint with my state insurance commissioner BEFORE finishing internal appeals?

My health insurer denied a claim for a procedure my doctor ordered. I filed the first-level internal appeal three weeks ago and havent heard anything. Their letter said they have 30 days to respond and I'm coming up on that deadline with nothing. I know I still have the second-level appeal and then external review after that but this process is already taking months and I'm getting a $4,200 bill sent to collections next week if I cant show I'm disputing the claim.

My question is whether I can file a complaint with my state insurance department now, while I'm still in the internal appeal process, or if I have to wait until I've exhausted everything. I've seen conflicting things online. Some places say you can file in parallel, others say the commissioner wont look at it until internal remedies are done.

I'm also wondering if filing a complaint has any downside - like whether it makes the insurer less likely to approve the appeal, or creates any problems I'm not thinking of.