A bit more on the topic, based on some very recent (this week) personal research...
In considering this issue, I went back through a stack of my photos and came upon this one:

The picture, taken several years ago, shows some clown (

) happily TCing what appears to be an M4A1 with a commander's cupola.
And it appears there is applique armor in view, at least on the left side hull sponson.
Hmmmm. Needs more research, no?
OK, so here is some more detail, based on a visit earlier this week to the MVTF (Military Vehicle Technology Foundation).
Here is the vehicle in question:

It clearly has factory-installed applique armor on the left hull sponson.

It also has factory-installed applique armor on the right hull sponson. And also clearly does NOT have applique armor on the right turret face.

And yes, it has a cupola. But interesting to note, it does NOT have a loader's hatch.
For a point of comparison, here is the catalog pick of GHQ's M4A1 75mm "Modernized" (1943/44 upgrade) Sherman:

The lack of a loader's hatch on the Sherman I was investigating marks it as an older series turret than the turret on the GHQ model. Yet the applique on the right turret face should be more common in older turrets (before the new castings took care of the thinner armor).
Still, not every tank received every applique. But the appliques on the tank I investigated were clearly factory-installed, rather than field retro-fits. (Note how the side hull plates were cut to conform to the curved hull shape -- a characteristic of factory installation vs. field retro-fitting). Yet the turret applique was more common factory-installed, rather than field retro-fitted.
Now for further complications to the back-story. The M4A1 in my pictures above is NOT an M4A1. Rather, it is a Grizzly 1. The Grizzly was a Canadian-produced Sherman (built after they gave up on the indigenous Ram tank). The differences are minor, mostly in the interior fittings. One observable difference is that Grizzlies received the interior-turret-mounted 2-inch smoke mortar before US Shermans did (look for the small hole in the turret roof at the loader's position, above the "Black Magic" name). Seeing that mortar on an earlier model production turret (no loader's hatch) is a visual tell-tale of a Grizzly 1.
Since there is not reason to presume that Canadian production was synchronized with every upgrade in US production, the presence of the cupola, the lack of the loader's hatch, and no turret applique, really gives me nothing conclusive.
So .. after all that mumble-foo, I can only say with certainty that applique and cupola
may go together, at least enough so that I would not object to this model Sherman featuring prominently in my US Army in ETO, 1944/45.
(Oh, and I can also say that I like playing with tanks. Small scale, or large.

)