Hiring for a permanent position is like skipping dating and going right into marriage. For me, I need to be sure.
I’ve never seen this or tried it, but if I got a letter to this effect, I might seriously consider it if HR would let me.
If you apply for summer internship with a frank cover letter that, in addition to highlighting your strengths, says that you recognize that your lack of internships potentially makes you less attractive for a permanent position and therefore you are seeking a temporary position so that your employer can “try you before they buy you”, you might get some response. It shows an unusual self-awareness. It might help if you have an acceptance to a graduate program to go to in the Fall so that HR can properly consider you temporary.
Another reason that this might work is that in the defense industry, the fiscal year ends Sept 30th. Your employer can get your labor with a promise that they don’t have to support you beyond the end of the fiscal year. This is very attractive for projects that will end this fiscal year. It’s one of the primary reasons I seek summer interns.
Of course once you get a position, work like a dog, get noticed, and make such an impact that they want to buy, or at least provide you with a positive reference. I have definitely hired former summer interns that I wouldn’t have considered as permanent candidates because their academic background wasn’t quite up to my expectations. Try before you buy is a potential winning strategy for both parties. It also works both ways.