O365 migration where Exchange 2003 and 2007 coexist ?

I was about to do a O365 cutover migration from on-premise Exchange 2003, when I read the following:

You can’t migrate public folders directly from Exchange 2003. If you’re running Exchange 2003 in your organization, you must move all public folder databases and replicas to Exchange 2007 SP3 RU15 or later. No public folder replicas can remain on Exchange 2003.

That is from the following TechNet article:

https:/ /technet.microsoft.com/en-US/library/jj200758(v=exchg.150).aspx

So, if I install Exchange 2007 to coexist with Exchange 2003 and move the public folders, will that scenario be supported by a O365 cutover migration? or should I completely move to Exchange 2007 and get rid of Exchange 2003 prior to the O365 migration?

OR should I migrate the 300+ public folders to O365 some other way, skipping the Exchange 2007 migration.