Can I brew my coffee this way?

This is probably a really stupid question lol but I usually put the creamer into my travel mug, brew just enough coffee to fill the rest of my cup, and then pour it over the creamer. I like my coffee super super hot, but doing it this way, the creamer cools my coffee down way too much for my liking. What I'm wondering is, once I've added the water to my coffee maker, can I just put the creamer into the coffee pot and let the coffee brew into the creamer that way? I figured this way the warmer plate under the pot would heat up the creamer a little and then the coffee would brew directly into the creamer which would help gradually warm it up as it brews. Is this a good idea or no? My travel mug is not microwave safe and I don't want to dirty another cup every day (sometimes multiple times a day) just to warm my creamer up in the microwave.