Visigothic kingdom was glued into a spiral of revolts and dynastical rivalries from one hand, and not that concerned provincial nobility tempted by local revendications (as Count Paulus' revolt). No dynasty really managed to establish itself more than two or three kings before being crushed by a pretender.
Giving that claimants and revoltees didn't have a real problem calling outsiders to help (Franks in 632 or Arabo-Berbers in 711 being good, but not the only examples) I don't see why no or repelled invasion of 711 would change something there.
If not Arabs, Franks' intervention is another likely possibility (as Dagobert did in 632) and could end with a more or less pushed presence (especially with the contemporary Frankish expension). Maybe something akin to the Ostrogothic protectorate during Theodoric's reign, meaning up to placing frankish nobles at the head of some regions and/or treating some territories as an enlarged Aquitaine (as Gothia was IOTL, basically).
Would regional particularism still arise at the point to form Aragon or Portugal? It's hard to say. Obviously these are products of the reconquista, but you did have particularism and tentative to crave out similar kingdoms.
Regardless of the visigothic use of sub-kingdoms (trusted to brothers or sons) that was nevertheless interesting on this regard, you had already established particularism as within the province of Gaul (almost systematically and formally unconcerned by Councils) up to some claims to an "Eastern Kingdom" (by the aforementioned count Paulus) that covered the province of Gaul and Tarraconesa.
If Roderic's ground in 711 highlight regional solidarities (remember that his seat was in Merida), it could let the ground of a similar but western particularism and kingship (increased in case of Frankish takeover, that would be more focused on North-East).
Nothing set in stone, but the possibility definitely exists for both.
It doesn't mean Visigoths were doomed, of course, but their survival as an independent power depends heavily from the weakness and issues of their neighbours (there Franks and Berbers) while they were going down in a spiral of civil war. How would Spania look like at this point may be a bit different (more divided territorially to begin with).
I don't think that the Councils may have survived as a political-religious institution, at least not as a central one : a bit too useless and essentially tied to a prestige and legitimizing feature.
Now, I'm going to disagree with Archangel : the fusion of population was a thing at the late VIIth century, with the "gothic nation" being used for the whole of the peninsula. At this point "Goth" had the same meaning than "Frank" in northern Gaul.
Linguistically, you'd have obviously many differences : without Arabic and Basque influence (particularly present in Castillan), Spanish may looks a bit more as Italo-Roman or Occitano-Roman speeches, and without too many chanceries (that eventually set their own standards), you may end with less "official dialects" (meaning speeches beneficing from a chancery status) and less diverse speeches inside the kingdom.
I'd disagree with Delvetius as well : the blunt opposition between church and business is quite irrelevant, critically in a period where clerical lands and holdings formed prime commercial points (or at best, serving as piggy banks). While the religious drive would be certainly much different from Reconquista, it would still exist nevertheless more internally focused, more widespread rather than forming lines along reconquest phases.
I'd tend to think that while Betica would remain a wealthy place ITTL, it would suffer as the Mediterranean coast from the decline of the trade in this region and the disappearance of Byzantine economical presence. It wouldn't surprise me to see Galicia or Lusitania or even Cantabrias being akin to Seine or Lower Rhine basin on this regard (maintaining ties with Ireland, Britain and western Gaul)
Tarraconesa, would it be only tough its huge productive possibilities, may remain an important place but there again, Franks would have an easy time craving their own in Spain.