Can I work on Stored Procedures using LinqPad?

Of course you can. In LinqPad version 4.51.03 you can easily run stored procedures you have created using both SQL and C# Expression.

For example, after connecting to AdvventureWorks2012 database I can see all the stored procedures. Right clicking a stored procedure and choosing StoredProceedureName(...) drop-down, you display the stored procedure in the query window. You need to insert the parameters inside the parenthesis containing the ellipsis and run the query.

Examples are shown in the following two posts:

http://hodentekmsss.blogspot.com/2015/01/learn-querying-sql-server-2012-using.html

http://hodentekmsss.blogspot.com/2015/01/learn-querying-sql-server-2012-using_25.html