Yes- once fired brass, F/L re-size including adjustment for proper head space - bump back if needed, then check trim length. A standard SAAMI chamber will accept F/L sized brass using SAAMI spec dies provided brass head space & trim length is correct. Spring back (memory) near bottom of brass, that is work hardened, should be negligible provided SAAMI pressure limits observed; if exceeded by a certain extent loose primer pockets are likely.
For years I used once fired 7.62X51 (.308W) GI/LC (white cardboard box, red eagle having admonishment "not for combat use") match brass with no primer pocket crimp, fired from M1A (M14) match rifles used by various active duty Army rifle teams - cheerfully donated. For my M70Win action match rifle I used standard RCBS F/L dies with bump-back & a Vickermann seater die. No problem - standard load used 168 Sierra or Hornady bthp bullet with 44 grains of H380 (old lot) with many load cycles. I then got into turning necks & my 600 yard scores improved.
Thinking I had mastered this, many years later, I got 250 RCW 5.56X45 /.223 once fired brass & resized 50 to .20P (.20-.223) using a Redding .223 F/L bushing die with a .226 bushing. About 3 out of 50 stuck in the .20P chamber after firing and the extractor ripped the rim off. I then got a RCBS .223 Small Base body die and no more stuck cases after the first pass in load production. Some time later I discovered that my standard RCBS .223 F/L die also fixed the problem when used without the expander button. Possibly, hot loaded factory ammo fired in sloppy chambers caused the problem.
I don't see why modifying a standard F/L die by removing steel at the bottom & removing the shoulder & neck portion & preserving basic body taper would not work. F/L dies are real tough, hardened steel so I have not attempted this.