I agree with your contractor that it is not necessary.
In fact it would be better if you don't, in my opinion.
If it is not directly exposed to moisture or UV from the sun I would prefer to leave it uncoated so if it does absorb some moisture it will dry out more quickly, prolonging it's life.
After looking at your links, it appears you have purchased an unfinished wood top. It will need some sort of finish. You have a couple of choices, oil or a hard finish.
Oil finishes on raw wood will help keep the surface from staining and make them repel water. Oils can often deepen the color or actually alter the color as it ages. Oils need to be reapplied periodically to maintain protection. Not my first choice if going to be used as a work surface with paper, pencils, pens etc. Oils offer no surface protection from scuffing or denting. Something as simple as writing with a pen on a piece of paper could leave indentations on the surface.
The second choice would be using a hard overcoat like urethane. Urethane is absolutely clear and will help to preserve the original color. Once cured, multiple coats of urethane will give you a very hard surface that will protect the wood and resist scratching. It can be cleaned with any mild cleanser or even a damp cloth. if you want it to be really slick, you can use regular furniture polish on it. Trick is to use 3 or 4 thin coats of urethane, sanding with fine 200 to 400 grit sandpaper between coats. If done well, it will be smooth as silk and give you superior color lock and surface protection. the other nice feature is that if it gets a little trashed over years of use, you can sand and recoat, will look like new.
Obviously putting urethane finish is a bit more work than an oil finish, but the protection is much better and the maintenance much less. Be careful of linseed oil products as they can stain objects that may come in contact with it over time,(paper, clothing etc.) and can sometimes leave an unpleasant odor for awhile. Tung oil is much better than linseed oil.
Best Answer
NO. Linseed oil will not work on freshly sealed wood, it will not penetrate and will just lay oily on the surface until it partially dries into a gooey mess.
The benefit of products like Thompson's is that they last longer than natural oil finishes (although any claims of better protection are unproven, and in my opinion dubious). If you prefer linseed oil then you will have to wait a few (3?) years, then be prepared to re-apply the linseed oil annually. Better to just reapply the Thompsons every 2-3 years IMO.