I certainly think it's possible. I don't know if they can ever get a bigger market share than Amazon but a lot of people who buy stuff online type it in to google search first and then and add words like buy, shop, where can I get, etc.... to their search terms.
If google tweaks its algorithm to prioritize themselves over others then it's possible.
In fact they might have done this already. I just did a search for "boxing gloves" as an experiment for this answer and Google shopping results show all Google products on rank 2 of the results.
Amazon was ranked 8 for the search.