I don't know about Chase, but I can tell you what happens with the BA Amex.

Usually, you will have 1200 BA miles deducted from your Chase balance, which will put you into negative with Chase. I.e. you will need to spend $801 dollars before earning any more miles. Your BA miles already earned won't be affected, not bonuses etc. On this forum, it's been discussed that triggering a BA Amex voucher with a refundable purchase (and then getting it refunded) does not invalidate the voucher.

tb