The short answer is no.
You don't need to have a logo to trademark your brand. In fact, the logo is just one of the brand elements that you might consider trademarking. But there are others and some of them are more important. For example, the name of your company, the names of your products, the names of your services, taglines, and yes logos. All of those are just the brand elements and all of them can be and sometimes should be trademarked. So, there's absolutely no reason why you should wait until you have a logo to start protecting your brand. There's absolutely no requirement for you to submit a logo with your trademark application. In fact, the names are more important to trademark than logos. Logos change all the time whereas names usually stay the same. And also logos are usually made around name so why would you work on a logo without knowing that your name is protected. Though the proper way to do it, well there's two proper ways to do it.
The first way to do it is to start with the name, start protecting the name. Make sure that the name is trademarkable and start the process of trademarking the name. Once you know that the name is good to go that's when you get your logo design around that name and then you protect the logo as well. The second way to do it is yes you start with both the name and the logo. You get a trademark specialist to check if both the name and the log are available. And if they're both available then you trademark both the name and the logo. And if there is a problem with either the name of the logo of both then you go back to the drawing board and come up with a new name and then you come over the new logo. But again, don't wait until you have that perfect logo to start the trademarking process. It's often too late but never too early to protect your brand. And you want to start with the most valuable element of that brand and that's usually the name.
Disclaimer: Please note that this post and this video are not and are not intended as legal advice. Your situation may be different from the facts assumed in this post or video. Your reading this post or watching this video does not create a lawyer-client relationship between you and Trademark Factory International Inc., and you should not rely on this post or this video as the only source of information to make important decisions about your intellectual property.