Would a big indoor plant improve the acoustics of a room?

It would help some, but you'll probably need more soft things as well.

It could help. I think an area rug would be more helpful though.

A plant might help a little, but isn't going to make that much of a difference. You need fabric, a rug, pillows, a ladder with quilts hanging on it, etc.

Thea: Maybe lay down a large area rug instead.

The hollow sound is caused by the acoustic signals reflecting off the walls, floors, and ceilings. The general suggestions above about soft things are true, but keep in mind that you need both enough things to help soften the reflections, but also the things used need to be sufficiently non-reflective for sound/acoustic waves to do what you want. So for the large area rug, you don't want a thin hard rug similar in texture to a car floor mat.

You can find lots of info on line from a DIY standpoint that provides more details. I did a general search for "DIY acoustic softening for bare walls" and several sites have more detailed suggestions for you.

I'm sure it would help

Wow, sounds cold and institutional. Why no fabrics? I get minimalist, but not to the point that it is so stark that it appears cold and unwelcoming, plants will help pretty up the place, but not do much to change acoustics. You need rugs, pillows, throws, etc. Is there a medical reason?