Yes
Most definitely! You don't want anything like a cup point digging into your backplate, if you do you'll risk raising a burr & not be able to remove the chuck from the adapter if the raised burr is larger than the mating clearance. The set screws aren't for holding, they're just for adjustment.
Normally the set screws are in the chuck & contact the adapter. I'm not sure how you are making your adjustable ER40, by the way you described, sounds like you are making it so the ER40 chuck fits inside the adapter & the set screws are on the adapter. No matter, same difference.
1/4" would be fine. ER40 collet chucks are very light. Even if you are converting one to an adjustable/Set-Tru type, I doubt it would weigh as much as an adjustable scroll chuck.
To give you an idea. My 6.3" Bison Set-Tru chucks use M18 set screws for adjustment & they weigh 21-25lbs. M18 is roughly .70" & they use M18 all the way up to their 25" chucks. The 6.0" Gator Tru-Adjust 3 jaw chuck I used to have weighed just under 20 lbs & it had M12 screws.
On my 5" D1-4 ER40 chuck that I made a Tap-Tru, I've never had it bump out of true having no adjustment set screws. IMO you can't really take heavy of enough cuts for just over 1" dia max to be able to knock it out of true. The mounting bolts on the face has plenty of enough holding power.
In case you don't know what I meant by Tap-Tru, the register on my adapter is slightly smaller than the ER40 platea. I just lightly snug the mounting bolts, tap the chuck true, then tighten up the mounting bolts. Plain & simple. Here's a pic I took of my ER40 plate when I finished mounting it. You can tell it doesn't weight much at all. And if you are making yours so the chuck sits inside the adapter, might want to add holes for a tommy bar. Comes in real handy if you don't have a spindle lock on your lathe. The style ER40 plate I got already had the 3 holes for the tommy bar. Lucky for me the size of the tommy bar fits perfectly on my super spacer as well so I only had to make one tommy bar.