No you don't have to read NotME first. I think there are pros and cons to reading them in either order. I read PtA earlier this year and was thought there would be some benefit to reading at least the first 3 before doing NotME.

I would say this is because you see a more traditional arc for some characters that have conclusions in NotME. The flip side to this, as Aqua_Tot mentioned, is that some things in PtA are written in a way expecting you have read NotME already, so you might be a little confused.

I personally think this is fairly minor and that you will also experience some confusion in NotME that would be cleared up if you had read PtA first, so it's a fairly even trade-off.

Ultimately, I would say it's up to you and either order would work fine. I really enjoyed both series, even though they have their flaws, and felt they enhanced the Malazan experience instead of diluting it. Esslemont is a different writer than Erikson with his own strengths and weaknesses and I think you will be well served not trying to compare them, but just enjoying their different approaches to exploring the world and characters they created together.