yes, many clients (light clients) do this. downside is a central point of failure (in your example blockexplorer.com) and privacy issues. Most of the android clients do it this way. Running a full blockchain-verifying client on a phone is overkill already and it will probably get worse in the future.
The important thing is that your light wallet should allow you to be in control of your private keys. This way you can always eject and go for another solution if the server that backs it is unresponsive. Blockchain.info and BitcoinSpinner (possibly also Electrum?) allows you to do so.