With New-MailboxSearch I can create an estimate which will allow me to see the data. The only issue I found was that the syntax for the command was a bit of a pain to figure out. If you were to do an export using the Search-Mailbox command, the syntax would be as follows:
Get-Mailbox damian | Search-Mailbox -SearchQuery “Size:>5MB” -TargetMailbox damianscoles -TargetFolder Export -LogOnly -LogLevel Full
As you can see, for querying large items uses the syntax -SearchQuery “Size:>5MB”. This enables me to find items over 5 MB. the rest of the script will dump the items to the target mailbox listed in the one liner.
Now how do we do this with New-MailboxSearch
get-mailbox “Damian” | New-MailboxSearch -Name Damian -SearchQuery -estimateonly
For search criteria, if you check the HELP for the New-MailboxSearch command, you get this for -SearchQuery:

Search-Mailbox has this for the -searchquery switch:

If you notice that Search-Mailbox provides a link for the Keyboard Query Language (KQL) needed for queries. However, New-MailboxSearch uses the Advanced Query Syntax (AQS). However, the help for the command provides no clue as to what we can query for. After a bit of research I stumbled upon this very helpful link http://msdn.microsoft.com/en-us/library/aa965711%28v=vs.85%29.aspx
If you review the list, size is still listed as something that can be queried. If you review this reference page for AQS, you will notice the syntax is something like this ‘size:> 50’. The 50 is the number of bytes in size a message is. If you are looking for items for Office 365 migrations, you should use the number ‘size:>26214400’. Here is a real world example of what I used to create my report:
Get-mailbox “Damian” | New-MailboxSearch -Name test -SearchQuery ‘size>26214400’ -estimateonly

After the command has been run, you need to initiate the search:
Get-MailboxSearch test |Start-MailboxSearch

To check the status of your test, run:
Get-MailboxSearch test |ft name,status,sourcemailboxes,PercentComplete,ResultNumberEstimate,ResultSizeEstimate -auto

Notice that you get a report of the Size of these items as an estimate.
Once you are done with the estimates, you can remove the search with:
Get-MailboxSearch test | Remove-MailboxSearch
And you will get prompted to make sure you want to remove the request:

There are many uses to this command and it certainly can come in handy for Office 365 moves.
Notes
Don’t forget you need Discovery Management rights in order to perform these commands. Otherwise the commands will fail.
AQS Help – http://msdn.microsoft.com/en-us/library/aa965711%28v=vs.85%29.aspx