Can I upgrade to newer groupsets despite my frame not supporting internal cable routing?
Internal cable routing is not a requirement, as long as you have functional cable stops on your the frame, you should be able to cable up a newer cable group set without issue. In fact it should be easier than internal able routing, which can be quite fiddly to get the cabling to pass through restrictions.  

The primary advantage of internal routing is aesthetics, followed by straighter cable lines and less maintenance (because of protection). The latter two are possible, but are not a guarantee with internally routed cables as it largely depends on the design of the frame, and some of the recent internal routing schemes are clearly prioritizing electronic shifting over internal cables. 

A good example of the importance of implementation, is my winter road/summer gravel bike, which has decent internal cabling lines and for the most part is well sealed against the external environment, except for one weak spot which allowed water to dribble into the rear shift housing and pool inside the internal tubing by the bottom bracket. The pooling also brought fine grit and eventually cause  shifting to deteriorate substantially. It took me a while to track down the problem as this small area was hard to access and I only determined the issue after replacing all the internal tubing (as a last ditch effort). 

With externally routed cabling I would have been able to track down and fix much easier, as it is easy to access all points.  If you ride in poor conditions, and you don't have full length external cabling, there are also ways to better seal external routed shift cables (e.g., Shimano's cable end cap seals) making external routing more robust to poor conditions.

That just leaves aesthetics as the primary benefit of internal cable routing, and maybe straighter cable lines, but recent frame design seems to be negating this positive.