Hi Elliott -
I think the answer is yes, but that's much more complicated than anything I have attempted with JMRI. I use JMRI mostly as a control panel to control turnouts, accessories, and operating cars; an Arduino runs the trains but is limited to an ABS-like system That I developed.
But (if you haven't already) take a look at the Warrants section of the JMRI website - that's where they describe the automation capabilities. But it's so complex it makes my head spin!