No. You need to have enough in your account to cover any auto-investments you have scheduled. It’s a good idea to add a bit of “cushion” to your NZD deposits fluctuations in the FX rate.
For example, if you have a monthly auto-investment for $500 USD in Amazon, your fee will be $3 since it’s a fractional order (assuming Amazon shares don’t drop in price!). You might want to deposit something like $900 NZD a month to cover the fees and changes in the exchange rate. We have some examples here.