MySQL 5.5.8 InnoDB Foreign Key, JOIN performance We are using aws/rds, MySQL 5.5.8. all InnoDB.

For performance purposes, we have merged some data-elements into varchar fields; mini-sized int and date type fields; added covering indexes; de-normalized some tables to behave almost like key-value stores; shareded tables containing user generated rows etc.

We are also looking to further improve insert performance by omitting some possible foreign key relationships between large tables (2+MM rows) since our app layer does a lot of similar integrity checking and prevention.

My question is about theoretical join performance between two tables A and B, using a primary key on one side A.F1 and single row index on side B.F2. Since I could also define the B.F2 as a foreign key (over A.F1), I would like to know if such a join would be any "faster/better etc." with or without the foreign key constraints - all other things being equal (indexes, no other fields, no order-by etc.).

We expect a lot of read queries over such situations, and fewer inserts that would benefit from foreign key omissions.
Foreign key relationships are to enforce data integrity, not for query performance, that is what indexes are for. Also note that InnoDB creates an index on each column with a foreign key relationship.  

However I would recommend having the foreign key relationships to ensure that the data is always valid, especially when updating and deleting, which may become significant when you have to start archiving data.