Your application emails people when important things happen, right? 

If it doesn't it should. People like to know about important things (and it's the best marketing you could ask for).

Most people check email on their phones – among other places – and the best email is actionable.

…so they log in to take care of whatever you emailed about.

On their phone.

You probably have more mobile traffic than you think. And if you don't, you probably don't use email very effectively.

tl;dr: You need to support mobile, even if you don't.