Will my fountain pen dry out?

Hi! This is my very first fountain pen (received it for Christmas, and I hope to use it for university (I live in Aus, so start at the end of Feb).

I really want to try out the pen, yet I will only be able use it for a day or so just now. My family is moving house and I’m in charge of that, then I’ll be moving inter-state to my university. Therefore I’m not planning on writing during that time.

If I put the ink cartridge in now to test the pen, then pack it away for a month, will it dry out?

Fountain pen noob, thanks so much!