In a word ... no.
I contacted Honda UK and received the following reply
Thank you for contacting Honda UK.
At this time Honda have no plans to incorporate the Android Auto feature in to older vehicle year models.
In order to obtain the latest update for you vehicle, we advise contacting your nearest Honda authorised dealership. Updates for the Honda Connect system are released around June each year.
If you come across any errors on the mapping system, you can use the following facility on Garmin's website to report this - https://my.garmin.com/mapErrors/report.faces.
Thank you for contacting Honda UK. If you require any further assistance, please do not hesitate to contact us again.
The only way I have found to run Android Auto on the Connect is to root your phone, download Android Auto (version before v3 otherwise won't work) and a special app to mirrorlink the Android Auto. Run mirrorlink and it works via mirrorlink on unit. Would imagine similar for iPhone but not sure. Not tried it myself yet as phone under warranty.