It says they count as not having moved in the movement phase.
Grim resolve says that if they didn't move, they fire with reroll 1s.
I would think it applies.
The stratagem makes no distinction at all, making it only applicable for the purposes of bolter drill, that I can see in the text.
err I think you're mistaken friend, here's the strat almost word for word
(1cp) Steady advance
...Until the end of the phase, for the purposes of the bolter discipline ability, that unit is treated as if it had remained stationary.
This strat is purely so that you can move and still rapid fire bolter weapons, it mentions no other weaponry besides. I hope you didn't get a misprint!
Our dedicated chaplain power, however, states that models can shoot with any weapons as if they had remained stationary, being able to benefit from grim resolve and/or bolter discipline.