Do permanent profiles affect a Soldier's chances of being selected for promotion?

Absolutely not. For as long as the soldier continues to display that he/she is able to achieve higher standards. I was selected for promotion to both, SFC and MSG with a P2. Why? I continue to score 90+ on my push ups. I do things that show that I am physically fit for duty. I am not able to do sit ups, but I do compete in 5ks when possible. Have you ever biked 600 miles on a weekend?? Win a bench press competition? There are a plethora of other physical challenges that can show that you are fit, and combat ready.

In my experience, it really depends on a few things. I've watched as soldiers who work desk MOSs and their careers didn't slow down much due to temporary profile limitations. However, I have watched many of my scout and tanker brother's get stone walled at SSG and they were more than qualified to move up the ladder. I think that it all really depends on the MOS of the soldier and what the particular limitations may be. Even though regulation states that if it doesn't interfere with the ability to pass a pt test that it shouldn't reflect negatively, we all know just how far some of those regulations really get followed...

DA PAM 623-3:
For Soldiers with permanent and temporary profiles who have been cleared to take an alternate APFT, enter “PASS” or “FAIL” for the alternate APFT as prescribed by health care personnel and the date of the APFT. The APFT may include an alternate authorized aerobic
event (walk, bike, or swim). No comment about the rated Soldier’s profile is required.

So no it shouldn't because the profile shouldn't even be mentioned unless the Soldier has a permanent profile that prohibits them from taking an APFT all together. Then those are left blank and the rater describes why there is no "pass or fail." Perhaps having a permanent profile that prohibits you from taking an APFT would affect promotion but I would think at this point anyone who is at that point is probably being medically discharged.