It was a bigger deal with the Model 3 because Tesla sales people were telling folks the full $7500 federal tax credit was a risk to run out by June 2018. Also, there was a lot of demand for a lower priced Tesla so a lot of folks wanted to be first to own.
Neither of the above is a factor for the Y so I don't see much reason to pay a deposit now just to lower the risk of waiting several months longer than those who paid the deposit.
Lastly, the Model 3 has a majority of owners who are first time Tesla owners so demand was pretty high. I'm not so sure if that will be the case with the Y, but I suspect a decent percentage of Y buyers will 2nd Tesla owners so it would be easier to wait for delivery and we all know the risks with quality issues on the first couple thousand cars made, given Tesla track record.