Is there a downside to using InDesign for web mockups?

Nobody really cares if you use a ball peen hammer or a claw hammer to build a house. All we care about is the quality of the house when you're done. How you got there, and the tools you use hardly matter. Use the tools most comfortable to you.

That's my advice anyway.

While I agree with both answers to a small extent, some tools are meant to be used certain ways and others aren't. You can use a screwdriver as a hammer because you have that in your pocket, but no one is going to make a real case that it's the best way to do it.

The tools you use absolutely matter, especially in the real world. How quickly you make things properly affects your deadlines and deliverables, they allow you to properly and accurately deliver assets to developers. Photoshop vs. Sketch vs. Illustrator vs. Fireworks: that's a good argument because they're all tools that can do similar things appropriately.

Would you layout a whole book in Photoshop just because you know it better? No. You learn to use tools by using them, and the sooner you start using them the sooner you'll be proficient. Move in to Illustrator, Photoshop, or Sketch as soon as possible.

In my opinion, the only reason to use a specific tool would be if you were on a design team where the majority of the designers were using something different, and it would hinder the workflow if you didn't make the switch. I think you should stick with what you know, so that you can perfect your workflow and eye for web design. Once you consider yourself a solid designer, then you can experiment with different programs.

I used Fireworks for years when everyone said it was subpar and not good enough. Now I use Photoshop and Sketch, and haven't opened Illustrator in months.

I agree with everything Aaron said, my original answer was from a position that I have no idea what Jacqui's web/mobile/app design experience is, how familiar he is with the many screen resolutions, how responsive pages should be laid out, how basic interactions should work and how to think through a user flow. Sometimes it can be easier to learn the fundamentals if you don't need to learn a different software at the same time. At least he can get his ideas down with InDesign currently and progress from there.

However, If you have a pretty solid understanding of these things, then you should certainly move towards a piece of software that you're going to encounter in the professional world (PS, IL, Sketch). You should also have some familiarity with HTML/CSS3 so that you know what's possible in development. You'll be working with PSD's (or .sketch files in Sketch) and creating slices for the devs, along with dealing with icons, sprites etc. And you could be using Illustrator for icons as well. Most likely you won't be dealing with PDF, but that's just in my experience.

Sketch is high-fidelity and meant for designing and not just wireframing. It's a main purpose of it's programming: to scale to great sizes so you can retain quality for bigger and bigger screen densities. And what's the PDF connection? Why are you making a PDF for web design?

As to why you'd use Illustrator over InDesign for web design: better illustration capabilities, manipulation, exporting of assets, scaling, pixel previewing. But, I also wouldn't recommend Illustrator over Sketch or Photoshop for web and UI design. My overall point would be that you don't use InDesign for creation of anything web related, you could only ever use it to maybe layout things you've created elsewhere, so why use InDesign at all?