When BATFE launched its new ATF eFile system enabling the electronic submission of NFA documents on-line, particularly ATF Form 5320.4 and trust paperwork, they tested the system's ability to reduce the backlog of this paperwork. At the time of eFile's launch in August, BATFE selected a number of FFL/SOTs for monitoring. Their goal was to determine whether the documents uploaded by these gun dealers could result in a tax stamp issued within 90 days. 

That test appears to be a success.  After three months' wait, those tax stamps are now reaching those gun shops. 

It remains to be seen if/when all electronic filings will receive this speed of processing. Also, it seems filings made in hard copy via US mail must still endure a backlog of many, many months despite the hiring of additional manpower by BATFE/NFA Branch.