If I submit my AMCAS application on June 1st, will med schools see my summer grades if I update my profile? (the summer classes are between June 5 - July 31, so I get my grades early August).
I don't know what you mean by 'update your profile' but they will not see anything unless you send them updates. Some schools are open to this and some are not, or at least not until after an interview. Before you matriculate you will also have to send a final transcript as well.
Some secondaries are asking for any additional info (i.e. new grades) just fyi - if your grades are good the secondary will be a good time to inform schools.