Hey there, Ilias_DaPro!
You would be able to install and run programs from your external HDD (via USB) on the computer, however, the performance of the software might be a lot slower when compared to an internal SATA HDD. I'd recommend you to make sure that you get at least a USB 3.0-compatible HDD, this way you'd ensure that the transfer rate would be better than through the USB 2.0 connectivity.
If you're planning to upgrade to a secondary internal HDD in the future, I'd suggest you use that external drive for backups of your system & data.
Hope this was helpful.

Best of luck!
SuperSoph_WD