Given the fact that most tanks do have the bracket/mounting plate welded directly onto the tank, it obviously is possible. But consider the regulations that govern ASME Pressure Vessel Welding. Not many home shops are equipped, nor or most hobbyists trained/skilled in this field.
Even so, it's not impossible. Just risky. If you understand the risks, and are willing to do the appropriate testing, there's little reason not to do it. But be aware that some states prohibit non-code welders from working on code required vessels. I would imagine a catastrophic failure resulting in an insurance claim would likely run into some problems if the cause were traced to a non code weld.
If there is already a mount on the tank, can you weld a new plate directly on top of it with the correct hole pattern in it? Or maybe even leave the "sides" and maybe an outer ring intact and weld on a new plate?
Even in the case of pinhole leaks, it is possible to plate weld a patch over the entire bottom of the tank, where rust usually causes these pinholes. Same rules apply though. Risk, skills, regulations, and testing. On another forum, there were several pages of yes and no opinions on this issue. Generally, most people seem to think it's better to replace the tank. On smaller compressors, it's probably not that hard to find an identical or similar enough replacement by sourcing a dead pump or motor at a surplus center or garage sale even. Larger tanks might be harder to locate, but probably could be had reasonably from a compressor service center.
