I think you can. Allen Gottlieb (SAF) is a convicted felon and I believe he had his rights restored. That may have changed.
In 1984, Gottlieb pleaded guilty to evading federal income taxes for 1977 and went to prison for about one year. As a convicted felon, Gottlieb was no longer legally able to own firearms. But he regained those rights through a federal government program which allowed felons to apply for "relief" from the "disability" of being unable to own weapons.
http://wafreepress.org/07/Q&A.html
In the P-F basket of deplorables.
Sounds like he might have gotten it in time, and Allen may have as well. But it looks like the option isn't currently available.
Although federal law provides a means for the relief of firearms disabilities, ATF’s annual appropriation since October 1992 has prohibited the expending of any funds to investigate or act upon applications for relief from federal firearms disabilities submitted by individuals. As long as this provision is included in current ATF appropriations, ATF cannot act upon applications for relief from federal firearms disabilities submitted by individuals.
[18 U.S.C. 925(c); 27 CFR 478.144]
Tim Allen's Federal Conviction for narcotics would preclude him from possession firearms or ammunition under federal law.
If those items are "live", an experienced federal criminal practitioner would likely advise removal of the same to avoid potential legal jeopardy.
For all practical purposes, absent a Presidential Pardon or specifically worded Commutation, there is no way to get firearms rights restored after a Federal Conviction for narcotics.
I am not your attorney. I am not giving legal advice. Any and all opinions expressed are personal and my own and are not those of any employer-past, present or future.