Automator can't currently do it. (Can't crop). I'm not a coder.
I am no coder either but I have played around with this to try and come up with a solution and I think you can semi-automate your workflow. If your desired result is to split the page into two separate files it wouldn't be too difficult. If on the other hand, you want to split the page and then merge the files so that you have two separate pages in one file, it would just be a little more manual work.
You can use Automator to take care of duplicating and opening the files into Acrobat. Then you can use the "Batch Processing" command found in the "Advanced" menu under "Document Processing" in Acrobat to automate the crop.
First create a folder and use the ScanSnap software to create a profile that sends scans to that folder. Then create a workflow in Automator using the following steps and then save it as a "Folder Actions plugin". Then you enable the folder action for the scan folder and whenever you scan anything into it it is duplicated and then opened in Acrobat.
1-Wait for User Action--Once you add something to the scan folder it will trigger the folder action, by using this step first it will prevent the workflow from running until you have finished scanning. You can put anything you want into the message part of the action, I used (Click “Continue” when finished scanning).
2-Get Specified Finder Items--Select the folder that you will scan into.
3-Get Folder Contents--This selects all the files within the folder above.
4-Duplicate Finder Items
5-Get Specified Finder Items--Select the same folder as in the second step.
6-Get Folder Contents--Same as step 3
7-Open Finder Items--Select "Adobe Acrobat Professional" from the "Open with" pop up. If you don't see Acrobat listed it may be because it is within a folder in the Apps folder. Just go to the bottom of the list and select "Other" and a standard open dialog will pop up.
Acrobat workflow: (Acrobat uses the term "Sequence" but it is the same basic thing. Also, you will need to make two "Sequences" one for "Left Crop" and one for "Right Crop.)
1-Select the "Batch Processing" command as described above. A window titled "Batch Sequences" will open.
2-Select "New Sequence" and give it a name. An edit window will open.
3-In the "Edit Batch Sequence" window make sure that the "Run commands on:" step is set to "Files Open in Acrobat"
4-Now select "Select Commands".
5-Another window will open and you can choose commands from the left column. "Crop" is near the bottom. Double-click on it to add it to the right column. Once it is in the right column double-click on it again, or click on "Edit", to open the settings window for the "Crop" action. Choose your settings and close out of all the windows.
Now when you scan something using the profile you created in the ScanSnap software it will be duplicated and opened in Acrobat. You then just have to use the "Batch Processing" command, select "Left Crop" and then "Run Sequence" on one file and "Right Crop" on the other. Once you save the cropped files I would move them to a new location so that the next time you scan they are not duplicated.
I hope this will work for you and please let me know the outcome.