One of the greatest influencing factors for a gym to incorporate Pilates is their return on investment. Gyms can view this in multiple ways: 1) Pilates can be a great stand alone revenue producing program option, 2) Pilates can help retain members who are looking for new workout opportunities in the gym, 3) Pilates can be fused with current gym programs such as Group X and personal training to create joint revenue (i.e. MVe options).
I really think your strategy should be dictated by your personal direction (classical Pilates vs. fusion Pilates) and the need of the gym you might be pitching. If you have the ability to bring them a plan that shows integrating Pilates on multiple levels, you might have a better chance of them seeing the potential $$ stream that could be brought in.
If you have a gym contact, it would not hurt to approach them informally at first, but if you will be pitching a gym where you do not have a personal contact, then I would insist that you have a detailed plan of action and anticipated ROI to show them.