There are tens of thousands of bee species in the world. (Bees aren't the only pollinators in the world -- they're just well-known, and also used to "target" pollination of some crops, such as almond trees.) So even if all managed European honeybee (the species which produces honey and which is kept by beekeepers) hives were to drop dead today, there would still be numerous bees in the world.
Are [honeybees] able to adapt to a life without human intervention?
Unlike most domesticated livestock, honeybees are quite capable of thriving without human caretakers (even after centuries of humans keeping bees, wild colonies are still estimated to outnumber managed colonies by a significant margin).
There is actually very little* that beekeepers can do for a hive's survival, and typical wisdom for beginner keepers is to "just let the bees do their thing" -- i.e., the less intervention, the better. Opening a hive causes disruption, annoys the bees, and potentially damages their comb. Harvesting too much honey can reduce their food stores (a balance which most beekeepers I know struggle with).
Hives often swarm in the spring (part of the colony flying away with a new queen), and those swarms don't tend to gravitate naturally towards manmade hive boxes -- they will end up in hollows of trees, abandoned barns, people's attics, wherever they can find a suitable open space that they can fill with comb to build a home. Those colonies can be relocated to a hive when removed by a competent professional, but they aren't necessarily "happier" or "safer" or "healthier" there -- just out of the way, and not going to get killed by a allergic homeowner who doesn't want to deal with thousands of stinging bees in their crawlspace.
* Occasionally checking for and treating for pests (varroa mites, hive beetles) is good for hive maintenance, but this is infrequent; even a well-monitored hive is susceptible to infection and collapse, to the chagrin of many beekeepers.