Part of its success I think will depend on how much they plug it at the end of Peston links/analysis/reports on the ITV News bulletins, and likely Good Morning Britain as well. Particularly with Jeremy on as the guest next Sunday, I think they need to get Robert on GMB a couple of times this week to offer analysis, and then end with mention (and slide) of who's on Peston on Sunday (along with time and channel) at the end. The kind of thing they do very well, and often, in America.
http://media1.s-nbcnews.com/i/newscms/2015_39/1235156/mtp_msnbc_hillary_promo_09_27_2015_7642585a119893ad7025e2ca44b1a204.jpg
That's not visually the best promo I've ever seen, but it's still an effective promo tool when included in other programmes (including usually Saturday evening editions of NBC Nightly News). They also run ads, social media etc.
I haven't seen ITV News recently, but if they're not they should also make a point of saying "Osbourne said on Peston on Sunday" rather than just "told ITV News" or "told our political editor Robert Peston". There's absolutely no guarantee that people being aware of the programme will lead to them watching, but I think this is the kind of programme where awareness it exists will be the issue. It also has the advantage that some people will be willing to watch Marr and then Peston - it's really Murnaghan it's competing with for viewers, if not Marr for guests. Having watched the first episode, if Peston can continue to deliver high profile guests (likely more than one politician a week, though) and actually get something out of his interviewees the programme could develop into a meaningful success. Profitable? Probably not. But it could help strengthen the overall output and perception of ITV News and Good Morning Britain.
I thought the ability to put some viewer feedback/tweets to the interviewee was actually a useful feature, particularly when other politicians tweet in. And Allegra seemed to add a lot more to the programme than 'screeny' would at first suggest.
Peston, however, needs to become sharper and more confident in his interviewing. He was stronger on Newsnight in part because he didn't have as long to ramble (though that never seems to stop Evan Davis

), but he either needs to be more concise here because time is precious, or allow guests to attempt to fully answer. I actually thought that was one of George Osbourne's better interview performances, and I can't tell if that's because he was given too much (unchallenged) room, or because Pestons manner and skill got something different out of him. Osbourne certainly didn't feel too scripted, like he was reading talking points, which is something.
My only major issue with the programme was the set felt too much like a US late night talk show - and Peston's introduction/monologue felt far too much like he was presenting the Daily Show (including attempts at humour, graphics over the shoulder). I think they need to make the format a little tighter and conventional, and let Pestons instinctive personality and tone lighten the mood instead.
It might -
might
- also be interesting to see some 'representative' party members or grassroots supporters appear every once in a while in the Campbell/McVey position, given that internal divisions within the Conservative and Labour parties seems to be having more influence on the leadership and direction of those parties right now than voter opinion. As Iain Dale points out, they should also be careful to ensure EU balanced guests.