To a degree, yes.
I spent the bulk of my formative handgunning years as a reloader and Magnum revolver shooter. I thought of .357MAG as being a nice medium-bore, medium-power revolver caliber. I looked at .44MAG as being a "more serious" caliber, when "power" might be needed. The hubris of youth.
Shooting slow-fire for leisure/target range enjoyment is one thing, but being able to exert sufficient recoil management to control and run any particular handgun at speed, while maintaining accuracy during shot strings, is going to mean the felt-recoil effect is going to be a consideration.
This is one of the reasons why there's been a return to using 9mm among LE agencies in recent years, after the .40 S&W had eclipsed the 9 for quite a while. It's easier to train groups of new (or just 'average') shooters using 9mm, for its lesser felt (and actual) recoil.
On the other hand, continuing to develop and refine handgunning skills using a .40 pistol makes shooting a 9 seem "easier".
Not the same as going from .357MAG to .38SPL, or .44MAG to .44SPL, but you get the idea.
Now, as far as what might constitute "handle with enough accuracy"
for you? Not something I could know. Not unless we were on a training or qual range and I could observe you while you were being put through some increasingly demanding quals scenarios and drills. Targets and timers tend to tell us things we might not realize.
You could look around for a local IDPA event if it interests you, as that might tell you a bit more about your guns, your gear (holsters/mag carriers) and yourself (skillset). Might give you an opportunity to become acquainted with more skilled folks, too, and perhaps open the door to continuing your shooting development. Might be fun, too.
FWIW, I also own a n "original" M&P 40C, a 2010 vintage model I ordered from the factory. It's a relatively mild-shooting compact pistol for a .40.
While I still favor .357MAG revolvers, I mostly carry .38SPL nowadays, but that's mostly because I carry a variety of S&W lightweight 5-shot snubs. Shooting .357MAG in the pair of M&P 340's I own can be a bit ... well, brutal. Especially as after a couple of cylinder loads, and definitely after a 50rd box of loads have been fired. Faster recovery using the +P or standard pressure .38's, too.
I continue to carry a variety of 9's, .40's & .45's retirement CCW choices, which means I continue to use them for range quals, drills and practice. The 9's are the "easiest" to run hard and fast. Less recoil. The .40's and .45's take a bit more effort and work, naturally.