Absolutely, yes. But possibly not in the way you're thinking.

The obvious disadvantage is the challenge of getting sharply focuses images while focusing manually. I have great vision, but I still struggle to focus sharply.

You can change the type of focus screen with some dSLR models and that can add some focus aids like split-circles and prism collars; it was one of the many reasons I upgraded to an 50D from a 350D/XT back when Canon still put interchangeable focus screens in the XXDs (before LCD overlays happened). But you still need good eyesight.

Will getting a camera with a larger viewfinder have any appreciable improvement in one's ability to discern focus from what they see in the viewfinder? Will going from pentaprism to pentamirror have any appreciable effect?

A bit. I have a 5DMkII as well as my 50D, and while the 5DMkII has a bigger, brighter viewfinder, and with the precision-matte focus screen, I can actually focus my adapted OM Zuiko 50mm f/1.2 when wide open accurately, since DoF is now depicted accurately. But it's not necessarily a huge amount of difference between that and my 50D equipped with a split/circle prism collar focus screen.

I am looking at a used canon 7D which has a much more magnified viewfinder over the T3 and is pentaprism instead of pentamirror.

The 7D's viewfinder won't be that much larger than the T3's, but it will be a little brighter.

But your best bet is an...

Electronic viewfinder

Mirrorless cameras have electronic viewfinders: ones that show the image the same way the LCD on the back of the camera does. But because it's digital data, the image can be manipulated. Exposure simulation is possible. As are manual focus aids, such as focus peaking, simulated split-screen, and magnification can all be used to help nail manual focus. Both my Fuji X100T and Panasonic GX-7 camera bodies have these types of features, and I find it slightly easier to use them than my alternative viewscreens in my dSLRs to manually focus my adapted manual lenses.

On a Canon dSLR, you can do some of this with the LCD, with the Magic Lantern firmware add-on, but it's not as convenient as having these features in the viewfinder.