No, that would not work.
Group and Merge is like a select distinct on a single stream. Merge Data Streams is a simple way of collating all records from multiple inputs.
The way to do what you want is not to use two readers but to define a lookup against the data you want to join against and use a Lookup and Return processor to bring the data together. If you are doing a 1:M lookup you can then use a single Split Records from Array processor to create a record in your stream for each looked up record (a 'join').
In some cases - if you just want to join the data together before processing it rather than checking consistency etc. - it makes sense to do the join in the snapshot by specifying the snapshot as SQL or using a View... obviously this approach assumes direct connectivity to the DB though.