Hi Randy
This is handled between the modem and the network. You have to try it out. Keep in mind that not all the networks are behaving the same way, eg i have a massive problem with receiving sms on a MKR1500 while in a finnland based network everything seems to work fine.
You can configure the handling of the sms storage (on SIM on internal memory etc) with AT commands to the ublox modem. RTFM. Keep in mind that the modem is built for proper power up/shut down which is not realistic with a arduino setup (We just cut power, right);=) So my recommandation is to write a configuration setup for the modem if you need non standard values for the modem setup.
Ergo: Try out.
Cheers