You can apply 4x4 transformation matrix (Transformation matrix - Wikipedia) to components via API: 2017 SOLIDWORKS API Help - Transform2 Property (IComponent2)
If you give me some sample matrix I might be able to create an example for you.
To start with a basic example, say you want to translate a cube from its position with the matrix:
1 0 0 1
0 1 0 2
0 0 0 3
0 0 0 1
So is doing this tangible without Solidworks motion or Solidworks simulation (just using Solidworks professional)
and would I be able to get solidworks to read the file containing the matrix every X units of time (e.g. every 1 second)
to check for any updates in its position
Please take a look at this example: Load Components Presentation Transforms From CSV File . It reads the CSV file with matrix like this:
And applies this to components as per the file. The components are moved in space with a help of presentation transform (i.e. it will work regardless the mates you have defined)
I will add another example which shows how you can do the real-time animation so you can modify them as per your needs.