Does Router Mode matter after launching website for real?

Hello, I downloaded Local today and had to use the LocalHost Router-Mode to get it to work. I tried turning off the Windows IIS, and Site Domains Router-Mode still didn’t work. I also found something in PID3900 listening to Port 80 called mqsvc, but I did an internet search about that and it looked way too important to turn off, so I left that on.

Anyways, does the Router-Mode in which we develop our WordPress site matter at all once we launch our site through whichever webhost we choose eventually? For example I have my domains currently with Dreamhost and looks like they support WordPress quite a bit. But will having a LocalHost Router-Mode going mess things up in the real world?

I plan on making an e-commerce site with 3D model viewing (found at least a couple WordPress plug-ins that say they can do that).

Thanks for any help!