to perform routine maintenance on your hose bibb to keep it from dripping?
If you are worried about an occasional splash, your pavers will be fine.
If you think you might be leaving the faucet open for minutes at a time on a routine basis, then yes - tie it into the downspout drain or make yourself a dry well using something like a 12" square clay flue liner - dig down 2' to make the top flush with your new patio and fill it with pea gravel.
Or not.