In my experience, this is something a lot of “consultancies” (really, software outsourcing and staff augmentation firms) want to do, mostly as a way of absorbing bench time. It rarely works, because it gets treated as a second-class priority. Client work is easy money with obvious returns; product work requires long-term investment with uncertain returns.

(The advantage of product work, of course, being that you’re no longer selling time for money, which is a volatile, highly competitive market with limited margins.)

I’ve seen a lot of companies try this, but not seen any succeed. I’m guessing it’s because account management and sales is so different from product management and sales, and because the products are rarely staffed full time. I’d start by looking at those two elements.