Kinda. So you would run Bitcoind like this bitcoind -datadir=.bitcoin -port=88888 -rpcport=99999 -rpcallowip=127.0.0.1 -rpcuser=bitcoinrpc -rpcpassword=password -blocknotify=
where is whatever command you want to run whenever you receive a block.

An Example:
bitcoind -datadir=.bitcoin -port=88888 -rpcport=99999 -rpcallowip=127.0.0.1 -rpcuser=bitcoinrpc -rpcpassword=password -blocknotify="bitcoin-cli getblock %s > block-%s.txt"
%s in the command is replaced by the block hash automatically by this flag so you would literally have %s in the command wherever you need to have the block hash.

I think that should work, although I am testing it right now and will get back to you when that runs. Edit: It works.