Does TCP keepalive refresh the timeout on a NAT?

I've read that NAT routers "assume a connection has been terminated if no data has been sent for a certain time period."

I've also read that TCP keepalive packets usually shouldn't contain any data.

So my questions are:

1. Are the above statements true?
2. Do NAT routers consider empty TCP keepalive packets when reordering/cleaning their tables?

I'm asking this because I need a reliable connection between two endpoints where both of them have to be able to detect and react to connection problems. I know that I might just implement a keepalive mechanism myself but I want to know whether the TCP implementation could be used for that.