There’s no reason why you shouldn’t be able to do that.
Since you’re new to JUCE and somewhat new to C++, you might want to spend some time experimenting with the individual components you’ll need to use before starting your actual project.
Typically the doing of things is not hard, the trouble starts when bringing things together with a user interface. An ill thought out design, or inexperience with a component (visual, messaging, or audio) can quickly turn what seemed like a decent application design into a nasty mess that’s hard to maintain or extend.
Why not just try to get a hardcoded audio file to play through JUCE’s audio classes first. Once you’ve got that working, a simple single tap delay effect on live audio will cover pretty much everything you need to know about recording, buffering, and streaming audio.
As a side project, start working with the user interface components. Don’t try and write an actual UI for your app though until a) you’re comfortable with getting messages cleanly between components and your main code, and b) you know how your audio code is going to work and what it needs to pass too and from the user interface. Otherwise you’ll just end up hacking and rewriting code, which is frustrating, and not a useful, or fun way to learn coding.