If it is a full IOS-XE upgrade, then no, you will need to restart the stack to run the new code. Remember that all the switches in the stack must be running the same code version.
If it is a SMU (Software Maintenance Upgrade), then it may be possible to upgrade a module without restarting the stack, but you will probably have some downtime, depending on the specific upgrade. The 9300 series was designed so that separate modules of the code can be individually upgraded, but as far as I know, Cisco has not yet released any such upgrades.
In any case, you should always anticipate needing to have some downtime when performing a software upgrade on a switch or switch stack (including switches that support ISSU), even if it is only a few seconds. You should only do such work during a network maintenance window.
Cisco has many documents regarding upgrading software on the 9300 switch series if you simply search.