Hi InstaDry,
This is possible - Work orders are stored in the Activity Table in Method (work order line items can be found in the ActivityJobItems Table). You could utilze the API to query the Activty Table to retrieve only those work orders assigned to a specific user for a specific date range. From there, your app can maipulate the data as required and push any updates back into Method.
Please post up any additional questions you may have on getting started with this integration.
Cheers
Jon