Can I delete the Watch app without unpairing Apple Watch? I have an Apple Watch paired to my iPhone. I don't use the apple-watch.app often, so I'd like to remove the app from my Home screen.

Are there any consequences if I remove the apple-watch.app from the Home screen, such as getting my apple-watch unpaired or unable to load iphone-dependent apps?
The apple watch app on your iPhone will not let you remove itself unless you unpair the watch first. 

So technically, no. As it is essential for the operation of the watch. What I did was just make a folder named 'Apple' and dump all Apple apps that I don't use often but somewhat essential for some things into that folder, like Weather, etc.