Mario Brothers : The reality
No, Mario was not a plumber. I'd say he probably worked in the sales and marketing department or as the chief of the administrative functions of the Mario Bros. Plumbing Corporation (dba Mario Bros. 1/2/3/Super). Luigi probably did most of the grunt work which explained his calm and unaffected demeanor: If your love in life is what you do and you don't have to worry about the details, how can you not be consumed with bliss(as Luigi was)?
This is probably the best sibling working relationship you can imagine. Given Luigi's constant state of bliss and Mario's generally amicable and reasonable demeanor, or what can be inferred from his cheerful 'Here we go!' attitude towards missions in Nintendo 64*, I can't imagine many disagreements occurred.
The one underpinning of all these accusations is that historians accurately interpreted Mario's size. We see him as small as Bob Hoskins in Super Mario Bros the movie and as large as Lou Albano in the Super Mario Bros Super Show. Assuming that somewhere between the two was Mario's real size, he would likely be 5' 8" tall and around 220 lbs. It's actually the shorter height that would play a bigger problem than the weight. I'd think someone built a bit like an apple would have no ability to get under a persons sink and their short alligator arms would just make for a comical display for anyone watching from the kitchen. Something like flipping a turtle on it's back, or a 3rd grader with a full backpack.
* In the Nintendo 64 release of Super Mario, Mario is finally put into situations that can be realistically completed by a person of his physical composure. True, in the Mario Bros 2 release, there's a pretty good chance he was able to get involved (and the character bias shows the same) in most of the work, but may not have been ideal for some. It was really in this 64 bit release that he could truly be believable as a character. Given the size of the pipes in the original Super Mario Bros and the again in the Super Mario Bros 3 release, it was highly unlikely that his somewhat portly frame would have been able to enter most, if not all, of the warp pipes.

