Cannot add items to Powershell array

It sounds like what you are really trying to do is relate data to create a small report. You are dealing with data coming from different commands so you need a property to join on. In this case I would look at the LegacyExchangeDN AD attribute and the LegacyDN property returned by Get-MailboxStatistics. The code might look something like:

$DisabledUsers = @{}

Get-ADUser -SearchBase 'ou=User Disabled Accounts,dc=test,dc=com' -Filter * -Properties 'Title','legacyExchangeDN' |
ForEach-Object{ $DisabledUsers.Add( $_.legacyExchangeDN, $_ ) }

$DisabledUsers.Values.SamAccountName | 
Get-MailboxStatistics |
Select-Object DisplayName, ItemCount, @{ Name = 'Title'; Expression = { $DisabledUsers[$_.LegacyDN].Title } }

This will output something like:

DisplayName   ItemCount Title
-----------   --------- -----
Mr. Smith        113576 Executives

If you would rather it go directly to a CSV file simply add the Export-CSV command after the Select-Object command, like below:

$DisabledUsers = @{}

Get-ADUser -SearchBase 'ou=User Disabled Accounts,dc=test,dc=com' -Filter * -Properties 'Title','legacyExchangeDN' |
ForEach-Object{ $DisabledUsers.Add( $_.legacyExchangeDN, $_ ) }

$DisabledUsers.Values.SamAccountName | 
Get-MailboxStatistics |
Select-Object DisplayName, ItemCount, @{ Name = 'Title'; Expression = { $DisabledUsers[$_.LegacyDN].Title } } |
Export-CSV -Path $env:userprofile\desktop\DisabledADUserTitlewithMailbox.csv -NoTypeInformation

I would've used Get-User from the Exchange Management Shell, however it doesn't have the LegacyExchangeDN as a returned property. It does have SamAccountName, but using it would've forced me to bridge everything through Get-Mailbox. At any rate, this is a very common technique to use a hash table to reference related values in a different collection.

I'm sure some additional work will be needed to get the report just right.

An aside, try to avoid using the += operator to append arrays. The best way to get an array is to let PowerShell provide it as I did above. However, if you can't get around it the most common alternative is an ArrayList. Like most things there are several ways to go about it below is just 1 example.

# To create:
$ArrList = [Collections.ArrayList]@()

#To Add a value:
[Void]$ArrList.Add( 'ValueOrObjectHere' )

Note: Documentation / discussion of += and ArrayList's are easy to find with the Google machine...

Update:

Addressing Errors Noted in most recent edit:

The first error is basically impossible. Forgive me but I must assume you made some mistake to generate this error. LegacyExchangeDN should always start with '/o=...' and they key cited by the error was 'ADCDisabledMail' . Also LegacyExchangeDNs are naturally unique in Active Directory, so there's almost no chance you'd have a duplicate. As such, I made no effort, and none is warranted, to prevent such an unlikely error.

Note: If you are repeatedly testing the code you have to recreate the hash, $DisabledUsers = @{} else the hash will exist from the previous run and duplicate key errors are a certainty...

The second error, they 'key cannot be null' might be due to non-mailbox enabled AD accounts in the referenced OU effectively causing the LegacyExchangeDN attribute to be null for those users. Hence, null key.... You can avoid that by modifying the filter to only return mail enabled users:

$disUsers = Get-ADUser -Filter  { mailNickName -like '*' } -SearchBase "ou=User Disabled Accounts,dc=test,dc=com" -Properties SamAccountName,Title

Note: For reference, mailNickName is the alias propertry typically returned with Get-Mailbox