The Kelvin fits perfectly well into the Starfleet lineage of the Abramsverse. However, because of certain design elements of the Kelvin, I don't see it as a pre-TOS era ship. It doesn't fit into the Starfleet lineage of the original continuity.
Now, bear in mind that this is my personal opinion. So I expect plenty of insults and smart-ass remarks from the movie's fans. Therefore, to the STXI fans, pleast don't proceed under the false impression that your pot shots will in any way hurt my feelings.
First, there's the overall design. I like the design of the Kelvin. It is actually not a bad looking ship. But it doesn't look like a predecessor to the TOS Enterprise. And given that the Kelvin is supposed to be from the original TOS universe, it should at least bear some resemblance to the original universe's design style. This dissimilarity to anything that came before proves, at least to me, that STXI takes place in an alternate universe with its own continuity completely separate from the original that we know. Then there's the size. According to Captain Pike, the Kelvin had 800+ crew. Oooookay. That's a LOT of crew. That means that the Kelvin was at least TWICE as large as the TOS Enterprise, the flagship of Starfleet, of 30 years later. That makes no logical sense. For example, the NX-01 Enterprise from 2151 held 80+ crew. It was a small ship. 100 years later, the Enterprise under Pike held 200+ crew, later enlarged to 400+ under Kirk's command, yet the exterior size remained the same (presumably, crew quarters were double-bunked). That is logical progression of size and crew compliment as time and tecnology progresses. To add an absolutely enormous, 800+ crew starship into the lineage 70 years after NX-01 and 30 years prior to the NCC-1701 makes absolutely no sense. Think about it, the Kelvin, according to the dialogue and sheer number of shuttles aboard, was at least ten times as large as the NX-01. It was also about two times as large as the TOS Enterprise. What would be the logic in increasing the size of starships from little NX-01 size to gargantuan Kelvin size and then reducing back down to NCC-1701 size ships? And then later increasing again to Galaxy class sizes by the 24th century? It makes no sense. To me, it shows the writers' lack of respect for TOS in that they simply did not care if the Kelvin didn't fit into the original universe. Then there's the hull plating design. On the Nx-01, the hull plating was very symetrical and clean looking, yet it looked older than the NCC-1701. The Kelvin's hull plating seems randomly slapped together. There's no symetry to it. That's purely an aesthetic view, but it looks out of place to me.
Now, I know some are going to say something to the effect of "who cares? It's an alternate reality.", or "the Kelvin was a colinization or survey ship, it needed to be huge with a crapload of shuttles and lots of passengers." To that I must reply, there was no dialogue or action that gave any impression that the Kelvin was a colonization or survey ship. According to what was seen and heard in the movie, the Kelvin was just another Abramsverse version of a Starfleet ship. There will also be some who invariably will say, "we don't know what Starships looked like in the 2230's." That is true, but we can extrapolate using the NX-01 and the NCC-1701 as bookends and filling in the gaps. Logically, the Kelvin doesn't fit between the NX-class and Constitution class in the original universe. One can rationalize all day long that it's a movie and it doesn't matter. But one can not ignore the on screen evidence as compared to what we know of the origial universe.