Thanks! asyncio and aiohttp works well so far. But this particular example (music bot) uses synchronous bindings to MongoDB so it's not fully async. There are asyncio bindings for Mongo, but I haven't tried them.
I have another bot (https://github.com/szastupov/whatisbot) which is a client to wikipedia and asyncio makes much more sense in this case.
In general, think asyncio is inevitable in current world of APIs and micro-services.