Calling them tells you nothing in regards to your status. In fact, they aren't even quoting expected turnaround due to their workload.
You'll learn one of these three statuses, and it actually won't tell you anything about the length of time from the call until the form gets to you:
1) Not in the system.
2) Pending on X date.
3) Approved.
or alternately:
4) Being returned for errors.
5) Rejected.
Your check can clear and you may not be in the registry system for a couple to several weeks afterwards. You may go pending and you could transition to approved immediately (unlikely), or you could be in pending for a few to several weeks, or months. You can be told you're approved, and it may take 1-3 weeks to actually get the form back.
The status does not tell you where you are in line, as you can be pending as of May 8th, but there may be 24,000 forms ahead of you -- or three -- they won't say.
You can call, but I just wait it out now. I did call recently because I sold a SF suppressor to a man in Ohio. I felt obligated to give him a solid update, even if it doesn't mean anything overall, directly from the NFA.
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