DLLs can have positive and negative impact on performance. As with all performance questions you should get data before committing to a strategy.
Huge headers / huge code / slow compilation does not mean slow performance. It's often the other way around: that slow compilation is because you've given the optimizer a lot to work with. And simply rearranging your project won't reduce the amount of code. You'll just cordon off bits so the optimizer has less to work with. You may benefit in project structure, but at the cost of optimization opportunities.
A lot of modern elegant C++ is templated and purely in header files. That allows inlining as the optimizer sees fit. Breaking code into separate images will prevent optimization across image boundaries.
Consider the development cost of using DLLs as well. Interfaces across DLLs present a lot of complications. For example templated / header-inlined code should be avoided in the ABI. It's the entire reason COM was invented: to deal with the difficulties of passing basic objects between DLL boundaries.
To try and answer the question, my gut feeling is that "No", breaking your project into multiple modules will do absolutely nothing to improve performance and is much more likely to make it perform worse. I say that with about 93% confidence. But as I said: The only way to properly answer your question is to measure.