The short answer: no.
That being said, take some time to try to make an informed choice about how best to proceed.
Are you hesitating because you would prefer to do the application yourself (because of interest or finances)? Ask for instructions and be sure to take the time to read them. Lineage societies often are quite strict in their requirements for certain supporting documents, specific formatting, and more. Failure to comply with the guidelines may result in your application being returned to you for additional information. If you are comfortable researching and with the guidelines you’re reviewing, you are likely fine to move forward.
Are you hesitating because you’d rather work with someone else? Don’t worry about moving forward with your initial plan! There are societies that will push for a specific genealogist. Unfortunately, a smaller number may even hold up your application if you don’t use their preferred person. (I’ve seen it happen.) The vast majority are making referrals for one of three reasons: 1) they’re trying to build their own income stream (the Mayflower Society currently does research in house); 2) they’re trying to make your life easier by having an established referral list; or 3) they only know know a limited number of genealogists who specialize in lineage society applications (most often the large firms).
Ultimately, you’re seeking the best fit for you and your project. And it’s okay to seek that out.