No, that doesn't make any sense to me. Imagine you'd call someone with the flu and they told you they're sick too. You'd probably think you're bothering them or worry about them, you'd most probably not feel like it's nice you're sharing this experience with one of your friends...

I'd listen and talk to the friend, show some compassion. Being sick in bed can be lonely, having a few minutes of talking to somebody sounds like a nice thing in that situation.

Btw, when you repeat the exact words of somebody back, it's usually called parroting. It can be irritating to some people, others feel like the person repeating is listening attentively and it can be sort of comforting.