Did anyone try the combination Drupal 7 + apache 2.2 + mod_pagespeed + varnish?
Does it produce any problem?
IS Drupal own CSS and JavaScript aggregation mechanism needed if mod_pagespeed is used?
Have yet to test it out. I do know that domain specific code CAN be better in comparison to a generalized tool like mod_pagespeed; but I would imagine it would take a lot of effort to beat mod_pagespeed. mod_pagespeed should bring an improvement in comparison to drupal's core aggregation; you will get CSS & JS Compression among some other nice things.
In Drupal land we are working on improving the page load time. Here are some projects for that.
Long story short: Use mod_pagespeed today; checkout some of these projects in the future.
I can confirm that Varnish won't work properly if mod_pagespeed is enabled. I tested, if mod_pagespeed enabled, Varnish stop caching anything.
For reference: http://code.google.com/p/modpagespeed/issues/detail?id=232#c4