Can a 2011 MacBook Pro handle the new macOS updates?
From a performance perspective, should I just leave it there? 


No.  For two reasons:


You are running a 7 year old OS that is no longer updated since about October 2014.
4GB RAM is rather inadequate considering today's use cases.



  Or will
  I get any kind of benefits from upgrading to the latest (or a later)
  macOS?


The benefits will be numerous.  The most obvious would be increased application compatibility (i.e. Office 2016 and Phoshop CC just to name two) and increased security with System Integrity Protection (SIP).  

Your performance is mostly determined by hardware and you've already taken steps to increase speed with the addition of an SSD.  Increasing your RAM will have an immediate effect by reducing/eliminating the need for swap space.  While you SSD is amazingly fast compared to the HDD it replaced, it's still not as fast as system memory.

You may find this answer relevant:  My Mac is getting really slow, what should I do?

Personally, I have upgraded 2009, 2010 and 2011 MacBook Pros by maxing out the memory and upgrading to at least El Capitan all with excellent results.  There are no loss of performance with the upgrades.