There's no rel evidence either way. some think that anyone interested in playing Mario (GC) games would buy a GC, but I don't think that's true.
Obviously it's true of some people. While no one buys a GC for Mario Tennis, you do get two kinds of adopters regarding Mario:
1. People who buy the GC out of a general appreciation of the Mario franchise. These people then go on to buy a few Mario games later.
2. People who buy GC's for other reasons (Zelda, Mariokart, whatever), then buy Mario games because they're there.
The second type of adopter disappears if Nintendo goes 3rd-party. Mario Baseball was a top ten game last month in part due to the fact there weren't many other games on the Cube it had to compete with. Someone owning only a Gamecube isn't choosing between Mario Baseball and DMC3. Similarly, Metroid Prime 2 only had to compete with Halo 2 among people owning both Xbox and GC and people getting their first console. For people owning only a GC (such as me), Halo 2 wasn't even an option last Christmas, so MP2 was the "big" title. While 400K units isn't the greatest, if it had been an Xbox title, sales would likely have been lower, not higher.
The point is whether the increase in user base would mean more software income for Nintendo
No, the point is whether the increase in user base would mean more software income for Nintendo, period. You are completely overlooking the huge increase in competition they would have purely on the software front. Increasing usebase doesn't always mean increasing income. The classic examples are Sega (Xbox has a much larger audience than DC ever did, but they couldn't move sell copies of Jet Set Radio Future to save their lives) and the Viewtiful Joe 2. Nintendo as a software publisher has an effective near-monopoly on somewhere between a 10 and 18 million-person segment of the home console market. Has this worked? I'd say hell yeah; the only company on the planet that beats them in software sales is EA. #3 Activision trailed by a good 20% last month, and #4 THQ pulled around only half as much as Nintendo did.
You think it's because they make so many games? Guess again. In September, Nintendo published a grand total of four new games. Activision publsihed twelve.
DO NOT KILL THE GOOSE THAT LAID THE GOLDEN EGG.