Yes, you can do that, however then the programmer side on either the programmable stat or orig programmer would need to be set to 24H ON. You're effectively placing them in series (so they'd both need to be "on" for the boiler to fire).
I rather assumed (more fool me) that the reason for getting a programmable stat was that you'd be replacing the boiler with a combi eventually .... otherwise you could have just used a normal stat (no need to be programmable if you're keeping the orig programmer). Unless, ultimately you want to have more than the one CH zone I guess
Terminals 3, 7 and 8 refer to inside the boiler, if you look at the picture you've posted it appears that the boiler has had it's switched live wired into the live supply (and is hence on permanently).
I rather assumed (more fool me) that the reason for getting a programmable stat was that you'd be replacing the boiler with a combi eventually .... otherwise you could have just used a normal stat (no need to be programmable if you're keeping the orig programmer). Unless, ultimately you want to have more than the one CH zone I guess
Terminals 3, 7 and 8 refer to inside the boiler, if you look at the picture you've posted it appears that the boiler has had it's switched live wired into the live supply (and is hence on permanently).