Theoretically, you can solve any resource problems by adding more hardware -- and when one server isn't enough, you add more servers. But sustaining an inefficient solution by feeding it money starts to become impractical at a certain point.
On the one hand, rewriting an existing app as a scalable service is expensive, so simply deploying it as a terminal services solution seems a simpler path. But on the other hand, the solution scales dramatically more poorly than something like a web app.
First of all, a TS solution is "heavy" and persistent. A set of new processes starts for each user which persist until that user logs off, each of these consumes memory and processor time above and beyond that consumed by your actual application. And, of course, a TS application is much more server-intensive than a web app because all of the work, even rendering the UI, is done server-side.
The actual limits are tough to predict up front, but you should be able to do some stress tests while watching the resource consumption to get an idea from the trends. But keep in mind that there's a context-switching cost that only really starts to become apparent when you have a whole lot of running processes all at the same time. At some point, depending on the nature of your application, you may "hit a wall" before your CPU is saturated that can't be solved by adding more RAM. This is difficult to predict ahead of time.
Second, and perhaps more importantly, a TS session is dramatically easier to abuse than a client-server application. The difference is so significant that it's often not even mentioned. If you were planning a trip to Antarctica, people wouldn't bother reminding you to pack warm clothes; likewise if you're planning on deploying a TS solution to the public, people will simply assume that you understand to secure it every which way and plan for the worst. The various ways in which such a solution could go terribly bad are so numerous that they're not worth enumerating.
That said, if you don't intend to scale out that far, then this may be your most cost-effective solution.