If you look online, you'll see lots of serious people saying that paper surgical masks will not help protect you from wildfire smoke. However, I'm suspicious that this largely reflects a kind of signaling perspective and doesn't consider how effective they might be or under what circumstances and in what ways they might help.
That is, let's say surgical masks are 20% as good as N95 respirators which are 50% as good as P100 respirators at filtering out wildfire smoke (these numbers are 100% fabricated, although I think the ordering is right), then very responsible people will tell you don't wear a surgical mask because it won't help much, and if someone who didn't understand the details just heard "oh, surgical mask is good enough" they might wear one in a situation that lead to them being injured. Compare the lack of nuance in masking guidelines for COVID-19 purposes, and I think you get why I think something like this is going on.
But if a surgical mask was all you had, how much would it help? Enough to be worth, say, wearing one when you otherwise wouldn't wear one in order to help reduce smoke inhalation? Enough to be worth wearing indoors as part of a defense-in-depth strategy combined with HEPA air filtration?
Just to put some numbers on this, we can assume that burning wood has plenty of particles in the 0.2-0.3 micron range, which is commonly regarded as "the most penetrating particle size".
N95 masks meet the standard that they filter out 95% of these particles. https://www.cdc.gov/niosh/nioshtic-2/20023155.html
In the following study, the better of the surgical masks that was studied allowed 25% of the 0.3 micron particles through, which matches the 1/5th effectiveness you mentioned. https://www.cdc.gov/niosh/nioshtic-2/00210276.html
On p16 of this EPA handout, they absolutely do mention the hand-holding logic of having a false sense of security. But they also address the possibility that the mask can make breathing more difficult, contribute to heat stress, and that these masks:
They also specifically state:
So I think the serious answers to your final questions are: it would help by 25%, I sure as hell would, and maybe?