Office 365 Migration - Currently have EOP

Can you clarify what you mean by a non-persistent environment? For example, do your users connect to Exchange today using OWA only, or Outlook in 'online mode?'
The reason I ask is because Exchange Online works best when users connect either via OWA, or Outlook in 'cached mode.'
This presents a problem if your RDS/Terminal Server/Citrix environment is setup for Outlook in Online mode because usually it results in sluggish performance, slowness when switching between views (between calendars, especially if using delegation) and large mailboxes. One work-around is to use Outlook in Cached Mode but using a GPO to redirect the OST files to an external NAS/SAN so that the local RDS server doesn't have its HD fill up from all the OST files. Another option is if users previously used Outlook in Online Mode, convert them to start using OWA.
Or when you say non-persistent, do you mean more like VDI where the desktop gets refreshed/cleaned/wiped when the user logs off (or is that what you will soon be moving to)?
Regardless of the issues above, your question on whether to go Hybrid or not has nothing to do with persistent desktops or non-persistent desktops... Think about Hybrid as the right way to migrate Exchange on-premises to Exchange Online because it provides the best user experience during the transition phase. Just a few of the benefits are:
- Slowing migrate pilot groups to test functionality like free/busy and mail flow
- Unified Global Address List between cloud and on-prem (important if you are going to slowly migrate over days/weeks)
- SMTP domain name co-existence between on-prem and cloud, allows you to slowly migrate users while they get to keep their primary SMTP name the same
- Preserves the OST file, since the Mailbox GUID remains the same, there is no rebuild in the OST after the mailbox migrates to Exchange Online (preserves lots of internet bandwidth)
- Provides a friendly redirect to Mobile phones to automatically migrate their profile (in most cases)
- Provides a friendly redirect to OWA if the user tries to logon to the old OWA page
- There are other benefits to going hybrid but I recommend you engage a Partner or Microsoft Fasttrack to assist you (Microsoft FastTrack can give you some lightweight design assistance if you have more than 50 licenses, but they won't actually migrate the mailboxes for you unless you have more than 500 licenses, see their article here: https://technet.microsoft.com/en-us/library/office-365-onboarding-benefit.aspx)