Well, a militar victory for the Carlist side is very unlikely. We discused it some months ago with a POD where
Zumalacárregui doesn't die during the siege of Bilbao:
https://www.alternatehistory.com/discussion/showthread.php?t=151778
In short, due to its own nature the Carlists armies couldn't wage a long war, they had support only in some localized zones of the spanish territory and less resources than the Cristinos, not to mention the french, british and portuguese support to
María Cristina's side. Zumalacárregui genious could have balanced a bit the things, but he died too early to know it and how decisive it could have been.
But, most likely, the Carlists can get a victory
avant la lettre. If the absolutists are successful in their attempts to derogate the
Pragmatic Sanction, Carlos V would have been king of Spain. The most obvious occasion is during the incidents of La Granja in 1832.
Shawn Endresen has made a well put summary of the basic lines of the Carlist political program, though I'm not so sure about Carlos trying to retake Mexico. However I think the recognition of the mexican independence by Spain probably would be delayed. Furthermore, a Carlist regime probably would mean the diplomatic isolation of Spain from France and Britain, and perhaps also open hostility from these powers, thus the spanish economy is even more screwed than in OTL. It would have also inmediate butterflies in the portuguese political conflict, not too different of the spanish one in many traits.
Domestically, sooner or latter (and I think sooner than latter) the, let's call them "Isabelinos", are going to burn the country. Probably they could form an army (or something similar) in the Pyrenees with french support, while they could open another front from Gibraltar with british support, as happened, at some extent, (without official support of any power) during the irregular actions during the
Absolutist Decade (nothing important, conspirations and small raids, always with disastrous consequences for the protagonists). Most of the main cities (doubtless Madrid, Barcelona and Cadiz among them) would proclaim
juntas in the name of the rights of Isabel (if not something more "extremist") we would see barricades and disorders and if the enemies of Carlos manage to cooperate properly we could have a reversed Carlist war, with the difference that
"isabelinos" would have a slighty better base than OTL Carlists. We need to make clear at this point that liberals at this time and in this country is a very vague amalgame of groups and ideologies going from non-absolutist conservatives to democratic radicals and perhaps even some early republicans. Of course I don't mean that in this scenario the "isabelinos" are going to have the support of the "masses". In fact, I think we can expect apathy by the part of the majority of the population, specially in the rural areas (and that's a redundance, because most of spaniards were rurals at the time) with the exception of volunteers in OTL Carlist strogholds, obviously volunteers for the king's side. The key piece would be the army and here all depends on how efficient is the likely purge among the officers (it wouldn't be the first, by the way) once Carlos takes the throne.
Regarding the political fate of Spain under the reign of Carlos V. Well, first of all, I'm baised and I'm not very sympathetic towards the Carlists. In my opinion it would be a very dark hour for the country. Sure, OTL spanish 19th century is not at all the happiest possible, but a Carlist regime would be even worse. If it is long enoguh, I'm scared to think in the long-term consequences.
In the political spectrum, I suppouse that means that
maybe the future spanish left will be more similar to the italian and french left (more jacobin-style centralism) than in OTL, where federalism has been always a relatively strong branch inside the spanish left while
probably the right wouldn't have kidnaped the originialy revolutionary idea of the National Movement. In the short-term, as Shawn Endresen says, we have a less centralized Spain (to be fair the centralizing tentatives never succeeded properly, but they created political tensions that would be very important in the ulterior spanish history) with an strong religious component, whose constitution would be the old Fundamental Laws of the Kingdom (in some sense british style, but that's a rough comparation) and a harsh repression and a uncomfortable problem for France regarding the exiliates.
Cheers.