Most bike tourists use lightweight gear - there is a lot of crossover between the two activities. However, there is a difference between a week long backpacking trip, and six weeks on the road across the country, especially if you plan to camp and cook. Unless you just want to cycle across as fast as possible you will have to think about extra clothes and shoes for evening wear, visiting friends, and sightseeing. Also, tools and spares, reading materials, etc. In some parts of the country you need to be able to carry quite a bit of water, which is very heavy. You don't have to carry much food since you can get it daily, so that helps, but likely you will still end up heavier.

Which leads to my next point - the Trek 1200 will work for credit card touring and even camping for overnight or week long tours, as Gobes mentions, but I think it is a compromise on a cross country tour. It is lighter weight and the components are designed for fast riding, not slogging along on roads that may be potholed. unpaved or in dirt. Tires, wheels, shifters and frame are all lighter weight on the 1200, and designed primarily for speed. It has a shorter wheelbase and chainstays, which may limit the use of panniers, and it probably does not have proper rack or fender mounts although there are workarounds for that. You will need a triple and the gearing may need to be lowered even more. Lastly, the shorter wheelbase and lower riding position will make for ride and handling that is fatiguing on long days in the saddle, compared to a longer wheelbase, and heavier touring bike.

That said, you can do whatever you want if you are willing to make some significant compromises in comfort, durability and the route you take. Sometimes we get too carried away with the equipment and forget that 90% of the trip will be dependent on your attitude and outlook. Whatever you do - enjoy!