No, because I also have an advantage when I only find coins. You have to play your advantage, and your advantage is economy. If you lose multiple of the first few rounds, it doesn't really matter.
When you get only coins in the beginning, your chances at finding 2 Star units earlier are higher, because you can purchase more 1 Star units in the beginning than someone who gets items, then hold onto them to match them up.
By default, you have more coins and/or units than someone who started with items.
When possible, sell units you do not need and start to gain interest.
Later in the game, your chances at finding Items will be higher, as you found coins in the early game, and the players who found items will have lower chances to find items and an increased chance to find coins.