If that was my gun I would repair it, but NOT by just welding back on the busted part. I would make a part about an 1" or more long of the same thickens and with the hole in it. Then machine off a matching spot on the frame So the hole was properly located. Bevel the frame and repair part and then weld in place. This would give a much larger weld area to share the load and the weld area on the bottom of the frame is non critical and only holds the grips and magazine in place.
Because.
Although you can weld the aluminum used for most gun parts, unlike steel or many other mild aluminums it will never be anywhere near full strength. The weld's heat affected zone will always be brittle. Does not matter if it is tig, mig or micro welded this will remain true. Micro welding is probably best because of the smaller heat effected zone so maybe on a none critical part, but I would never ever trust it in a critical area. Post weld HT will improve it somewhat. Notice how airplane are riveted and not welded thats because they use the same or similar aluminum alloys as gun frames. High strength heat treatable alloys.
Aluminum gun frames are usually 7075 or 6160
From the AWS (American Welding Society)
The 7XXX alloys are the ones that usually trip designers up. They are the very high strength Al-Zn or Al-Zn-Mg-Cu alloys that are often used in aerospace fabrication, and are supplied in the form of sheet, plate, forgings, and bar, as well as extrusions. With the few exceptions noted below, the designer should assume that the 7XXX alloys are non-weldable. The most common of these alloys is 7075, which should never be welded for structural applications. In addition, these alloys often suffer from poor corrosion performance in many environments.
A few of the 7XXX series defy the general rule and are weldable. These are alloys 7003 and 7005, which are often seen as extrusions, and 7039, which is most often seen as sheet or plate. (and used in bike frames)
6061 is more weldable but mostly only done in lap joints etc, because the welds are prone to the same cracking in the HAZ. If weld is where 2 piece are butted up to each other and the area between them filled with filler metal and that would include a crack, there is no other support area like when a lap joint is used to spread out the HAZ and increase the support area