There are a few consequences of this. One is that the Commission will have to create a rather extensive service to be able to handle the petitions - maybe around 30 people if you also want translations done and replies given in the original language.
Another part is that if the Commission would be obliged to take some kind of action, its test of the admissibility of an initiative will be expansive (which it might be at any rate) and should be open to appeal at the Court of Justice (in my opinion). Giving legal advice on admissibility beforehand should then be separated from the Commission (requiring the creation of a new quango) and should focus on narrower issues, e.g. whether the power exists, and should not be binding.
I think it is preferable to have the initiators themselves check whether their proposal concerns an issue on which the Commission can initiate legislation. It should only take about 500 to 1000 euros to have a lawyer give an informed opinion.
So, for instance, a petition might have to pay the Commission for the ex-ante legal advice, with the cost of the advice (1000 euros, give or take ?) being refunded if the petition obtains more than (say) 100,000 signatures.