I have recently disassembled and rebuilt two mid-80's bikes. One of them I bought from the original owner who kept it garaged and the other was a trade-in at a bike shop - history unknown. The interior of the BB shell of the first one is shown below - very little rust after 33 years. The second one (35 years old) had a little bit of corrosion in the BB shell and the seat tube - not enough to cause any trouble removing the seat post.

If treating your frame gives you piece of mind then go for it. Otherwise, since your bike is nearly new and you intend to keep it indoors you will probably be fine unless you live next to the ocean or douse your bike in winter-road saltwater.