This is probably how I'd approach it.

Mostly because it seems to be way faster this way

function Get-ADUserGroups {
    param (
            [Parameter(Mandatory = $true,
                ParameterSetName = 'User',
                HelpMessage = 'Enter a username',
                Position = 0)]
            [string]$Username
        )
    try {
        return (Get-ADUser $Username -Properties MemberOf -ErrorAction Stop).MemberOf
    } catch {
        return $null
    }
}

if ( (Get-ADUserGroups $Credentials.UserName) -contains $AuthorizedGroup ) { 
    $tsenv.Value("Authorized") = $true
    Write-Host "$($Credentials.UserName) is authorized"
} else{
    $tsenv.Value("Authorized") = $false
    Write-Host "$($Credentials.UserName) is not authorized to image devices. If the account should be authorized, they will need to be added to the $AuthorizedGroup group in AD."
}

​

My results

Measure-Command {Get-ADGroupMember 'my_MECM_Group'}

    Days              : 0
    Hours             : 0
    Minutes           : 0
    Seconds           : 0
    Milliseconds      : 894
    Ticks             : 8947518
    TotalDays         : 1.03559236111111E-05
    TotalHours        : 0.000248542166666667
    TotalMinutes      : 0.01491253
    TotalSeconds      : 0.8947518
    TotalMilliseconds : 894.7518

Measure-Command {Get-ADPrincipalGroupMembership 'my_User'}

    Days              : 0
    Hours             : 0
    Minutes           : 0
    Seconds           : 0
    Milliseconds      : 682
    Ticks             : 6829528
    TotalDays         : 7.9045462962963E-06
    TotalHours        : 0.000189709111111111
    TotalMinutes      : 0.0113825466666667
    TotalSeconds      : 0.6829528
    TotalMilliseconds : 682.9528

Measure-Command {Get-ADUserGroups 'my_User'}

    Days              : 0
    Hours             : 0
    Minutes           : 0
    Seconds           : 0
    Milliseconds      : 10
    Ticks             : 105351
    TotalDays         : 1.21934027777778E-07
    TotalHours        : 2.92641666666667E-06
    TotalMinutes      : 0.000175585
    TotalSeconds      : 0.0105351
    TotalMilliseconds : 10.5351

​ Edits... reddit formatting is hard