If the question is: Is an application built with a framework slower than native code ? Then the answer is: Yes, less or more, a framework uses abstraction layers to simplify the development process and it (Framework) may take some extra time than native PHP code.
Does that really matter ?
I think it is not a problem at all, not enough time (difference) that one can catch the difference and a good framework is also built that keeping on mind. If you use a good framework and also properly write optimized code then it's fine and you don't have to worry about it.
Depending on the size of your project you should decide what to use and for a big project I always prefer a framework. There are many benefits for using a framework, such as a framework at first helps you to do more with less code, gives you unified API/Tools to accomplish complex tasks easily with less effort. A good framework gives you build scale-able and maintainable application and most of those are well organised, tested and maintained by a community so you may get help from the community on many situations.
Also, when developing application with many team members, it is much better that everyone is working on the same known documented framework, which might not be the case with your own archive PHP code and a framework also unites the team members to a specific convention of writing code because everyone follows same rule provided by the framework. It's also easy to recruit additional team members anytime who knows that framework and new team members can easily fit into development process.
Since, you said about 100k users, well I think it's related with the database than coding, if you have an optimized database then it may give you query result faster and yes also depends on queries you write, they also must be optimized.
So, I think you should use a framework and obviously make the decision by discussing with the team members you have right now. Laravel is a good one but there is a different candidate only for performance/speed and that is Phalcon and it's different than others because it's a compiled framework (c library) and that's why it's faster than others and maybe the fastest one so far.
But still, you should think about Laravel or suchlike one because Laravel has so many ready packages and support community than Phancon and it's easy to find help for a well known, widely used framework. These are my opinions but consider to use a framework, it'll make your life easier.
Performance benchmark of popular PHP frameworks (Source):
