Will macOS High Sierra work with MacBook Pro from early 2011 with 4GB RAM and 2.3 GHz Intel Core i5? ?

Is Sierra worked on your MBP then High Sierra will work also. However, 4 GB RAM is the minimum required to run the OS. If you're running CPU/Memory intensive apps you would be well served to upgrade the memory. I run a 2011 iMac on High Sierra with 8 GB of memory and have had no issues. Your MBP can utilize up to 16 GB of memory.

If you do upgrade I strongly recommend you get the modules from Crucial.com or macsales.com.

It will work, but you don't have take my word (or anyone else's) for it. Read Upgrading macOS without fear and decide for yourself.

Yes it will work. If it works with Sierra you should be fine with High Sierra.

4GB of RAM I would consider the bare minimum for any modern OS