No, it's not possible as Excel drop-down lists do not support multiple choices. It has nothing to do with SharePoint or with your list, but it's a known limitation of Excel.
A workaround would be to use Access instead of Excel.
Sounds like you could manually copy the calculated column data from Sharepoint to Excel instead? (Unless you have so much data that this would be impractical).
Otherwise you could recreate the calculated column in Excel. The problem with calculated columns is that they need all the columns used in the calculation to be present; when the data is sent to ...