I don't see why that would be the case, it would almost be like suggesting that after Chelsea signed Arnesen from us we would let them sign our players cheaper. Would be no reason for Roma to all of a sudden accept a lesser offer just because we just signed one of their employees.
The only exception would be if there was some kind of clause in his contract that Baldini would know about that we wouldn't know about. I think that's unlikely to be a factor though as when players want out those clauses tend to get into the media "somehow".
To me it would almost be more likely if it went the other way, where Roma could insist on us not signing any of their players (perhaps apart from transfer listed players or players they approached us about wanting to sell) for a year or something like that as part of the agreement with us to release him. A kind of do not compete clause, I think we got one of those in the Arnesen saga, although I'm not sure.
I think any player in the Eresdivisie is available for "the right offer". Him signing a new contract probably ups their asking price though, that makes him a less attractive prospect compared to if he hadn't signed a new contract.
Just look at last season, Dempsey, Vertonghen and Holtby both had a year or less left on their contract, Dembele had a release clause I believe (and a year left on his contract?), Ade and Sig both wanted to leave and their clubs seemed to want to sell them. I can't quite remember what the situation was with Lloris, but for whatever reason we managed to pick him up fairly cheaply.