Can I close AE while Media Encoder is exporting?

if the i already close my after effect while rendering it on media encoder and open the task managerand saw adobe after effect is still running on the background, should i close that too?

The only time I know of that you should not use the AME to render comps inside AE is when you have an effect that is accelerated by the GPU like Ray-traced rendering and a very short list of 3rd party effects. I find very few problems with 3rd party effects but if your render times go way up when using AME it's time to do some digging. Ray-traced rendering times inside AE with a supported Nvidia GPU / CUDA card can be 50 times shorter than rendering the same comp with the AME. I never use Ray-traced rendering because there are so many more really good alternatives and Adobe is no longer developing CUDA acceleration because NVIDIA completely changed their development and implementation of that technology so building a project today using Ray-traced rendering may make it obsolete in the next release of AE. I can't afford the time or the luxury of building a project that can't be easily reused six months or six years from now. Just got a request to update a 10 minute text animation (lyric video) that I did six years ago. A half dozen graphics changes, one edited sentence and a new tag line at the end and a reasonable budget for the changes. If I had used now obsolete technology, think Ray-traced rendering, the budget for the update would have to go way up and my relationship with the client would suffer. These are all things you must think about if you are running a business and expect to make a living at it.