See this:
- http://en.bitcoin.it/wiki/FAQ#What_happens_when_someone_sends_me_a_bitcoin_but_my_computer_is_powered_off.3F
Yes, new blocks occur about once every ten minutes, so your client will download any blocks it is missing so that it has all the blocks.
The storage for the blockchain data files is now over a gigabyte and growing. The client allows an alternate data directory to be used (--datadir= https://en.bitcoin.it/wiki/Running_Bitcoin ) if the default storage location (e.g., C: partition on Windows) is not going to be large enough.
Additionally, there are other clients (e.g., Electrum ) which work differently and don't use a full local blockchain.