I am a straight razor newbie myself, but I can't imagine using a straight with a brushless cream would be a very good experience. I have been shaving with my DE razor for close to a year, and I wouldn't use a brushless cream with that razor either.
Is there some reason why you don't want to buy a brush?
Using a brush and an actual shaving cream/ shaving soap is a huge part of the overall straight razor experience. The results would not be as exciting, or anywhere near as good without a brush.
Also, in general you can get much better quality components for a much better cost, by assembling the kit yourself.
The only thing I can comment on on that page is the razor, which is a very nice shaver. I have done... maybe a dozen Dovo Best Quality razors and they are very nice shavers.
It does seem like decent value (especially if the razor is truly shave-ready) but you could probably assemble a kit for less... if you really needed to.
Probably a good plan. I've never tried one, but I've heard nothing but good things about Larry's razors. (And at any rate, at those prices you haven't much to lose!)