According to the theory, yes. Because of the ages of the characters, it it less likely that our three protagonists from Mother 1 would be who we think they become in Mother 2. However, I really do want this to be true.
It's likely possible if Ana had a baby at 17 or 18 if the game took place in 1980 (since Earthbound Beginnings say "early 1900's" and then "80 years later"). The first Mother game took place in the 80's. Some people say "late 80's" I believe. The original Japanese Famicon (2:07) version of the game, however, took place exactly in 1988. Ninten, Ana, and Loid were all 11 or 12 years old. That would make them born in 1976 or 1977. In Earthbound, we're not sure what exact year the game takes place since it says "199X" but let's say that it takes place as late as possible which is 1999. Ness is 13 in the game and if it took place in 1999, Ness would have been born in 1986. If you were to subtract 1986 by 1976, Ness and Ninten would have been 10 years apart. That being said, no, in my opinion Ness' parents aren't Ana and Ninten. Again, the first Mother game could have taken place in 1980; Ninten and Ana would have been about 18 or 17 if Ness was born in 1986 being slightly old enough to have a child. That's the least that could happen, though. I'd find it really cool if it were true.
Apperantly, the date was mistranslated in the English version to be in the early 1980s instead of 1988, so in the American version, it's definetly possible (or they had a child before they 17/18, hey it could happen).
It actually would make sense if dr. andonuts were loid, because even though he has gray hair in earthbound (and he'd probably be in his 30's then)it would make sense as he also has gray hair in mother.
This would actually make sense, considering Ness was given his hat at a very young age by his father. Then, Ana would have married Ninten in the years between 198X and 199X. And since both Ninten and Ana have PSI, then their child would also have PSI. If this is the case, then PSI has cemented itself as an inherent trait over the years, and it was also shown that Ness' PSI had started to show at the same age that he got his hat.
There is more evidence for Lloyd being Dr. Andonuts than there is for Ninten and Ana being the parents of Ness and Tracey, so I consider "Lloyd = Dr. Andonuts" as my headcanon. Drawing parallels between Ninten and Ana and Ness' parents is a stretch. Here are the three main reasons:
1. If Ana is Ness' mother, why doesn't she remember Giegue's/Giygas' name?
2. If Ana is Ness' mother, why doesn't she fight off Giygas' minions during the invasion of Onett?
3. PSI isn't necessarily inherited. None of the parents of PSI wielding characters are known to have it.
As for Ness' dad, we know very little about him other than he works away from home a lot, so there really isn't anything to go off of. Still, you can believe what you want to believe. That's the fun of having headcanons, isn't it? (Unless that headcanon is wildly unrealistic.)