Echeveria and Agave are succulents that trap rainwater between their hydrophobic leaves. Droplets last a long time in these crevasses.
Mosquito abatement requires avoiding standing water. They reproduce in water, in only a few days. To this end we are supposed not to leave buckets or tires outdoors.
Can these succulents thus host breeding mosquitoes?
There are various effects.
Mosquitoes search some stable water, so if there are other sources of water, they prefer other places.
Additionally, there is not much water (usually) on succulents to create dangers to predators, so the eggs are less protected.
Finally, succulents should be keep dry most of the time, they like dry climate.
So, I would say it will mostly be insignificant. But it mosquitoes pressure is high, try not to water succulents on the week you remove all possible sources of mosquitoes.
Note: This summer I had a strange feeling that some mosquitoes uses palms (the flower/fruit attachments, which keep a lot more water) to lay eggs. On the other hand, all animals requires water, so there are much more reservoirs than we see. Try to discover the one preferred by mosquitoes.
Although the genus Culex is usually characterized as laying floating egg rafts on still water, a new study suggests most species of Culex oviposit out of water.
In the genus Culex, oviposition is often generalized as laying floating egg rafts directly on the surface of the water, as reported for arbovirus vectors Culex pipiens L. and Culex tarsalis Coquillett, both members of subgenus Culex. The current work reports on investigations of exceptions to this strategy by species of Melanoconion, a diverse and mostly tropical subgenus of Culex, with many arbovirus vectors. Wild gravid females from Vero Beach, FL, were introduced into outdoor cages with open water, partially covered water, and emergent solid structures for oviposition. Three species, Culex cedecei Stone and Hair, Culex iolambdis Dyar, and Culex pilosus Dyar and Knab laid vast majorities (80–100%) of egg clusters attached to solid surfaces, although at different heights and angles, while Culex atratus Theobald laid floating egg clusters (100%) directly on the water. When offered mud, open water, and woody material, Cx. iolambdis laid 86% of clusters on nearly vertical surfaces of mangrove rootlets. Culex iolambdis eggs laid on solid surfaces hatched within 3–4 d or dried up without hatching. Results suggest that Melanoconion species utilize a variety of oviposition strategies, yet most species studied oviposit out of water. For some species, such as Cx. pilosus, this is a strategy for diapause and desiccation resistance, while for others, such as Cx. iolambdis, ovipositing above water may protect eggs from predators or being flushed from larval habitat. A summary of oviposition strategies in genus Culex shows that above-water oviposition is widespread and that the Culex egg raft paradigm needs reassessment.
https://academic.oup.com/jme/article-abstract/54/4/812/3105867
So, to answer your question, if your leaves are near a body of water, then many species of Culex might well lay their eggs on them but will need to breed in the nearby body of water.
There is too little water to attract mosquitoes to lay their eggs. You do need to worry about a kitty bowl full of water in the shade yet able to fill when it rains. But not the droplets on succulents. Leaving anything out of doors that can collect water and last for longer than a week is mosquito hatching water.
Where is it that you live? We've got friends in Alaska that can tell you what lots of mosquitoes are like. Just moist bogs, soils, rivers...and they have to fight clouds of biting mosquitoes. They have to have mosquito netting when out of doors or allow the mosquitoes to bite them a lot...when mosquitoes bite they give off pheromones that tell other mosquitoes to back off. Weird, huh.
edit: I will submit that mosquitoes will lay eggs in any water. A teaspoon of water? Those eggs will not come to fruition. No problem. That water has to be able to stand at least one week to become a mosquito breeding problem. A few drops of chlorine? Such as water troughs for horses and cattle? Droplets on a succulent? Not happening. Yes, the eggs last for awhile but to ever become a problem those eggs need to be IN water water or moist bog soils at least a week. Just keeping little pet bowls, old sinks, any kind of water collecting container dumped out is pretty much all that is necessary. Imagine living in Alaska, lots of swamp/bogs/rivers/lakes...tons of mosquitoes that most people in the continental U.S. have no idea of the swarms!
I'd be worrying far more about what is in that water than mosquitoes. If it is from a well outside the influence of Aluminum ad Phosphate companies, then great. If it is tap water, highly infused with fluoride? That is a huge worry and needs investigation. Chlorine dissipates. Not a big deal...but fluoride?
Healthy people, healthy animals are able to deal with these diseases. The immune system of animals is powerful. When the animal (human) has a depressed immune system that is when problems arise. That is when cancer becomes a problem. Our immune systems are very amazing.
