Not directly, but you should be able to script something that triggers SQLCMD (a free Microsoft tool) with the correct parameters.

That being said, it is MUCH easier to pull data on a frequent schedule, vs pushing on demand.

I'm actually looking into testing this SQLCMD utility out. Do you have a particular example of using a script to trigger the utility? 

I'm actually looking into testing this SQLCMD utility out. Do you have a particular example of using a script to trigger the utility? 

Is this being done externally and not through customizer?

I'm fairly new to Sage (peep the username) and I'm not exactly sure what you mean by that. I was planning on putting a script set to the event of the "Accept" button in Customer Maintenance, that would then somehow trigger this SQLCMD utility, and call a stored procedure that would pull the data from our Sage db and pass the results in as parameters into our custom program's db. Connecting those steps together is where I'm getting stuck.

Google can show you how to call a command line (%COMSPEC% ...?) from a VBScript. 

The actual command you construct by referencing guidance from: "SQLCMD /?"  entered at a command prompt (after installing the program, free from Microsoft). 

Example:

sqlcmd -S SQLServer\Instance -d MAS_ABC -E -Q "exec spYourProcedureNameHere;" -o %TempLogFile%

Be very careful with this when running such a thing for Advanced / Premium to ensure you understand where it  is running based on how it's triggered from Sage, and the security context used.  I have never used this technique directly from within Sage, so I can't provide insights for that.  A manually clicked button script would be much safer than trying to set up an event trigger.