Real-time PCR delay in Cq due to insertion SNP in primer
As @WYSIWYG pointed out, having the indel difference in the 3' end can be informative, but I'm having a harder time finding evidence in the middle of the primer.  Putting the mutation/indel at the 3' end will change the ΔCT.  To do it well, you need wide coverage on your mutation site. 

I think that it is possible that there could be a difference with a mismatch in the middle of a primer, but it wouldn't be as obvious as if it were closer to the 3' end.  Unless there was some serious reason why you couldn't put it there (ie Tm below 45 on the reference) that sounds like poor primer design.

I will note I am certainly not a qPCR expert, and I don't think the question has been directly researched (as you surmised).  Again when I've looked for Indels before (was doing some interesting stuff with HLA types...) we used larger primers for the qPCR.  

If this doesn't answer your question satisfactory, is there an initial reference you would have us look at?  I imagine things like good quenching and other factors could pull out some significance when comparing two templates (one with indel one without), but again, it's kind of odd to put the mutation in the middle.

Edit to comments:
1: I think the Cq delay is going to depend on things like length, sequence, and mutation.  There may be a grand scheme formula/algorithm to predict the delay, but I don't know of one, and I couldn't find it if it does exist.  Most of the graphs and differences I've seen have been big enough that it convinced me that it was significant.  I don't know if this is like flow where you can sit and argue all day about the biological relevance of 40% to 30% of a particular group.

2: Sorry I didn't have time to come in and give an adequate summery of them.  They are, as you pointed out, tangential to what you're trying to do, but do in fact address the problem through their methods.  I will attempt a better summery as I have time (I've got a grant on I'm trying to get done by Tuesday, so probably after that).  If you have any clarifications to the question to add, please do.

3: This may have grown from the general perception that it was needed, and that I aim for the highest Tm I can generally manage without structure problems being introduced.  I also have the luxury of not needing to worry over the cost of ulta-mers.  It also could have come from history of working in BACs years ago.  Longer primers always increased my success rates when I was knocking out cassettes.