Heh, I just moved here from the US last month and had an HSBC account... Also had a 401k cash out I dealt with!
HSBC branches in each country are considered seperate banks, e.g., HSBC USA, HSBC Singapore, etc. The only benefit you get is the ability to use any HSBC ATM with *no* fee for currency conversion; that is an extremely useful benefit though.
For HSBC to work the way you assume, you need an HSBC Premier account. In Singapore, that requires a minimum deposit of S$200,000 in order to not pay hefty fees.
Anyway, my solution was to have my cash out deposited directly to my HSBC US account, and then just hit up the ATM for S$1200 every day (daily ATM limit of US$1000), and walk over to the DBS ATM and deposit it. Took a while

I also charged as much as I could to my US Amex card and paid the bill directly with the account.