Of course, you may choose to if you'd like, but doing so will ruin your street market.
For whatever reason, cucumbers and mayo appear to completely take over the street market after they are unlocked. Since they are used in a relatively small number of recipes, it's not currently worth it to unlock them if you are using the market as a source for longer term items such as onions and potatoes.
Just trying to save newer players from my mistake. For more on this (or just to see lots of sad cucumber-filled pictures), check the later pages of this thread.
In short, it's a trap!!