Engineers,
If you are going to use a half coupling, then normally you would just make the hole a little bigger and drop it in. The dis advantage of this in your application, is the fact that your tubes are so similar in size. The inserted tube would significantly reduce the area of the main tube/ pipe. You would also have an area where you fillet welded around without full penetration, that would leave a place for contaminants to collect inside your tubing. I notice you are using sanitary connectors , so I am presuming you want to keep the insides clean.
Your alternate method of just laying the coupler on the tube and filling the gap is also not a good one, because you will end up with a rough surface inside the tube, which would have to be dressed by grinding before the welder could go to the next stage, not to mention that having a gap there, that the welder would, have, to fill, is not a good way to make friends, and influence people.
You , or your shop, can quite easily make prepared ends on tubes/pipes, by buying a slightly longer coupler, clamping it in a vice on a milling machine, taking an end mill cutter the size of your tube, and cutting in the concave face then back milling to the desired length. You have to remember that on a joint with similar sizes the intersection will go as far as the centerline of the parent part. You then have to remember to prepare the joint for welding on both the parent tube and the stub you are fitting. the ideal is to have a Vee joint with as little material as possible at the bottom of the Vee so that the welder can put a root fillet in to seal the tube with as little weld material on the inside of the tube as possible and no gaps. You also have to remember that milling the end of the tube like this leaves an undesirable thin section at the sides of the joint farthest from the centerline of the tube which has to be removed by the Vee joint preparation. You should also remember that the hole in the tube/pipe will also not be round, but must be matched to the contour of the fitting.
B.E.
You are judged not by what you know, but by what you can do.