I'm really envious about offset accounts.
I wouldn't put that much in an offset account if I thought I could get significantly more by investing it in, say, Vanguard's VTSAX and VTIAX.
I would put my cash emergency fund in it because, hey, a 4% fixed return is pretty good when you need the advantages of cash flexibility and security.
But $200,000 is an awful lot of cash, particularly when it could be earning 10% on average elsewhere.
Unless I knew of a specific need for that much cash, I would put all but the cash portion of my emergency fund in the market.