Welding comments on this site make me face palm. Please, if you don't know what you're talking about, don't spread misinformation.
What the hell is "rare gas welding?" And aluminum is not typically soldered outside of electronics. Special applications, maybe; repairs, no.
I don't know what that upper is made out of. Newer ones are 7075 typically. The only way to truely know is have it tested.
When speaking of weldability of aluminum alloys in general, not receivers: 7075 is considered "not weldable." This is true for the entire 7XXX series as well as the 2XXX series. Why? Because these alloys are highly susceptible to hot cracking and stress corrosion cracking. Now, the term "not weldable" doesn't mean you can't place a bead on it or that it will crumble to pieces if attempted. It means the industry has deemed these alloys not sutable to be welded because of the two issues listed two sentences ago. These alloys are not to be used in structural applications where welding would be required. 6061 is welded all the time, it's a very popular alloy. Your next issue is the temper of the material. When you weld a tempered aluminum (usually t6 in off the shelf 7075 or 6061) you revert that temper back to T0 state. This affects the mechanical properties of the aluminum.
With all that said, could you Weld a 7075 receiver back together? Absolutely. Would it crack at the microscopic level? Yes. Would your eye ball notice or would that even matter in this relatively low stress application? Doubtful. Also, Receivers can be thin in places and could be difficult to weld if the welder is not skilled.
Looking at the costs, paying someone who knows what they are doing to weld, remachine and refinish the upper. That's going to put you in the realm of or over the cost of a new part.