when sewing - if I change the sleeve, do I need to change the arm hole?

I'm almost happy with my block pattern but the sleeve that came with it doesn't feel right.  For starters, it's only half-length and it just doesn't do it for me.

If I take a sleeve off something else, do I have to change the hole in the body of the garment that the sleeve goes in to match?  

To be honest, I don't even know if this is the right question to ask.  What is the question I need to ask here?

There are sleeves that come off the garment straight out. Lay some shirts flat, if the arms stick out straight they are that type.
There are sleeves that come off at an angle. Lay some shirts flat, if they point down, they are that type.

You can swap out the same type, generally, but not mix them, as the arm holes are made different.

You can add length to any sleeve that goes past the bicep without problems.

If it's a short sleeved or sleeveless shirt, you may have issues putting a long sleeve on it. Look at a bunch of long sleeved shirts, learn how the holes are shaped different for straight out or pointed down types, then if you have a short sleeved shirt, look at the holes, make sure you are putting the right type on.

Excellent points on the sleeve shapes. I'd have not thought to mention that. In my sleeve adjustment adventures, I have not been successful in changing the bodice pattern pieces to fit a different size sleeve,

BUT, I have sewn up a sleeve. Then separately, sewn up a shirt bodice. Then pinned the sleeve to the bodice. Sew them together neatly, then trim off the excess from the shirt. Now finish the seams, maybe by binding? All done!

Would simply extending the sleeve work? Using the pattern's seam line, adjustments can be made to the sleeve without alerting the bodice, at all. In my case, it doesn't work, because I actually need the armhole itself bigger, but length, width, and even shape of a sleeve can usually be played with, quite a bit.  

The shape of a sleeve needs to be consistent with the style of the top and bodice and sometimes different sleeve types are not interchangeable. For example, a fitted jacket with princess seams usually comes with two-piece sleeves and the sleeves are also narrower with high sleeve caps and need easing. A loose fitting coat or shirt with dropped shoulders have sleeves that are wider, flatter and no sleeve cap ease.

Before that, are the shoulder seams on the bodice spot on? If the angles or positions are off that will lead to wonky sleeves too.

Can you fix the original sleeves that come with the bodice? Are the armscyes too high? Biceps too tight?Twisted? What are the wrinkles look like? If you have a TNT sleeve pattern with the same armscye lengths, just pin the test sleeves on and see there are any improvement.