It's not a ridiculous idea, but you do have to construct the service/web app in a certain way.
I'd step back and ask why you're using them as 2 separate tasks in the server environment? Is there some sort of technical limitation that blocks you from either producing a single script, or even adding these 2 script tools into modelbuilder and having the output of 1 be the input to the 2nd? This is going to be the absolute simplest and most straight forward way to get what you want.
If you need to keep them as 2 distinct services, it'll be you who is responsible for getting the output from one to the other. Your web application will act as the glue between the two. Since your output is a layer the first service will either need to send the featureclass back to the webapp and the webapp will have to send the features back to the 2nd service or the 1st service will have to send the location the features are on disk (server side) and the webapp would pass this reference to the 2nd service.
Both these options arent great. Why?
Option 1 = the transfer of features when you dont really need to. (but you do need to because you have 2 services)
Option 2 = you're sending paths and information about the server back to the client. Even if its just the webapp getting this information and the user doesn't see it, I'd still consider this a minor security flaw as you're web-exposing information about the server itself.
So, again, what you want to do is possible, but I'd strongly suggest pushing both tools into a model and publishing that.