Rome will not attack the Canaries unless they conquer the rest of Mauretania south of Volubilis. Along with Germania, this is the best land Rome did not conquer, yet unlike Germania it's bordered by only the Atlas Mountains and the fringe of the Sahara, so there's not much opposition left there. The Anti-Atlas and the Sus River would then be the last frontier for the Romans in North Africa, but unlike other frontiers (like Caledonia), this area has argan oil (could be a nice trade good) and better farmland/grazing land. If we consider Britannia and Dacia, I think a conquest of at least the majority of Mauretania (the capital would be Volubilis, so the province would be "Mauretania Volubilitana") is just as feasible, if not preferable (Britannia tied up several legions for worse land than Mauretania). The Anti-Atlas and further south has the limit of cultivatible land (and thus the limit of any serious threats to Roman North Africa). Unlike Ireland/Hibernia, there's nothing comparable that would require legions to be stationed in the area, at least until the Canaries are enhanced by the volume of Roman trade to be on a level similar to the Irish.
OTL the Canaries were fairly isolated from the Roman Empire. TTL, Roman rule over coastal Morocco will mean there's a lot more trade, and thus Roman interference in politics there (just like in Ireland)
The effects of closer links with or outright Roman conquest of the Canaries could be huge. Bringing in tagasaste, a very nice feed crop native to the Canaries useful in drought-prone areas (like North Africa), will improve the value of North Africa to the Empire. Since holding down "Mauretania Volubilitana" will require more legions, North Africa gains a larger say in the Empire (OTL North Africa only had one legion, and compare Britain's legions and their influence in Roman civil wars). The Canaries themselves could be like Ireland, and be a center of Christianity.
After the Empire falls, I think the Canaries will be on their own, and fragment likewise, although the largest islands will dominate. Their history will be related to Mauretania, which will be part of a Romano-Berber kingdom. TTL, I think it's likely it will be Romanised enough it speaks "Mauretanian Romance" (intermediate between Iberian Romance and African Romance). The Canaries will be like Ireland I think. They'll have a lot of religious scholarship, they might re-Christianise some Berber groups, but they'll be pretty peripheral. This whole thing might cause a development in Canarian seafaring, so Madeira, Cape Verde, and even the Azores might be settled by Canarians (perhaps religious groups, like the Irish in Iceland and the Faroes). In the long-term, I think this area will come under the rule of the Mauretanian state, since they'll be divided enough to be vulnerable to conquest, and likely lead to a Mauretanian seafaring tradition which will allow the Mauretanians to be at the forefront of TTL's Age of Discovery. Of course, the Canarians won't go down so easily, and they'll be a potent source of pirates to the Mauretanians and Iberians for many centuries.
Long term, Canarians and their descendents will be largely assimilated into Mauretanian culture and like OTL Canarians, Madeirans, Cape Verdeans, Azoreans, etc. will be a key group of settlers in Mauretania's colonial ventures, wherever they may be.
There's some potential. Roman sailors occasionally visited the Canaries IOTL so certainly it was within the technical range of their abilities to go there. However, it was probably at the farthest limit of that range. The Canaries are pretty marginal economically as it is, relative to Roman technology and economy, so there's little incentive to pursue settlement and conquest at the extreme edge of the feasible without significant return. It has been suggested before in similar threads that in order to change that, you'd need to find a motive, most easily in the form of a valuable commodity from the Islands that makes their occupation worthwhile. Dyes seem the best bet, as indeed som can be harvested there and then sold in the rest of the Empire for a large profit. This could create also the puch to improve ship designs and general sailing knowledge making the trip easy enough to become routine, which is what you need in order to run the place as a Roman province.
However, there are limits. The Romans have much technological edge over the local proto-Guanche peoples, but the logistics of the conquests are not particularly favorable. There has to be a costly commitment.
Dyes, without a doubt, since that was the attraction of that part of Morocco OTL. Maybe some plant crop like the aforementioned tagasaste.