Can cryptocurrencies realistically support real-time micropayments and peer-to-peer transactions?

It absolutely can. One of the beautiful features of cryptocurrency is the ability to send across small values worldwide. There are a couple of points to be cognizant of.

• Gas fees. Trying to send $0.10 worldwide and paying $15 as gas fees serve no purpose. Some L1 blockchains, like Ethereum, Bitcoin, etc., have high gas fees; you might be better off using other L1 blockchains.
• General acceptance and liquidity. There may be an L1 blockchain that has low fee for sending money, but if it becomes challenging to on-ramp and off-ramp money from this particular blockchain, then it is something you need to take into consideration.
• Price volatility. If the currency value itself w.r.t. to fiat currency, is fluctuating wildly, then it might not be the best method for micropayments or P2P transactions.