The short answer is yes :-D
Are the files going into the same table, if so is there any need to identify which file or folder they came from. If not then you can just use Bulk Insert Task.
If the data is going to different tables or needs the file identifier on it then you will need to use a Data flow Task and the data transormation options to insert, convert and lookup column values
Are the folder names dynamic, If not then the BFI (Brute Force and Ignorance) method would be best: Create 10 FlatFileConnections
If they are dynamic then you can change the connection string of the FlatFileConnection string using an expression, but the formats of the source files must be the same.