He had a background on VB6 and Winforms but had done some WPF. Also by the sound of it he works building intranet LOB applications as he was saying that the apps would run internally and that they were currently using Click Once.
Anyhow, my answer got a bit long and turned into something of a rant but I think it had some decent point making it worth to cross-post it here :-)
Start of Answer:
To start with I'm wondering if there might be some confusion going on here.
There's actually no such thing as "Silverlight RIA", so lets clarify some concepts, RIA is commonly defined Rich Internet Applications, Silverlight is one of a number of technologies that can be used to build such applications.
However there's also the Microsoft technology WCF RIA Services, which is what I'm guessing you're referring to. WCF RIA Services were until recently known as .Net RIA Services.
WCF RIA Services (currently in Beta 2) has so far largely been targeted at Silverlight and is even hosted under the silverlight.net domain, which is probably where a lot of the confusion comes from.
However in theory it's not tied to Silverlight at all, and is just a technology on top WCF to provide easy data access for RIA type of applications, for a more technical overview have a look at this blogpost by Nikhil Kothari it was written back in March 2009 about .Net RIA Services, so it might be a little out of date but it will give you a good idea on what it's about.
After defining these terms, it's a bit tricky to answer your question "Is Silverlight RIA worth learning or should I stick to normal Silverlight?"
Silverlight is definitely worth learning, by the looks of things Microsoft is going to stick with it. The latest recommendation I heard from someone close to Microsoft, was to go with Silverlight if you can for new LOB (Line Of Business) Apps, if there's something Silverlight can't do, then look to WPF.
Coming from a VB6/Winforms background there will be a bit of a learning curve, but if you've already done a couple WPF apps then you're on good way already.
Silverlight for LOB? Silverlight 3 started bringing in more features related to development of LOB, like for example support for WCF RIA Services. It looks like this is set to continue in Silverlight 4 (due out first half of 2010), with things like support for printing and COM for working with MS Office applications. There's also coming more and more pre-made controls from various 3rd party vendors for many of the standard LOB type of functionality.
So what about WCF RIA Services? It's definitely worth having a look at, it seems to be the preferred way of data access by Microsoft. It provides things like easy access to authentication and data validation. However saying that it's still in beta and there has been some voices raised against it, around the internet so it's probably worth doing some research, before going all in.
Finally, you say that you're applications will be accessed internally but that you don't want the hassle of locally installed software, Silverlight fits that perfectly, just roll out the small Silverlight plugin to your users machines and you're good to go. Any changes needed, just recompile your project and deploy your .xap file to the webserver and it will automatically get pushed out to the users next time they use the app.
Sorry for the somewhat long and rambling answer, I hope it's helped answer your questions :)