No, there is no access to OS lounges on arrival, not even for HON. Never been possible in VIE. Showers do exist. In the passage to the WCs there is one shower for HON at the passage start and one shower for SEN at the end of the passage. In the C lounge there is one shower directly inside it. I cannot tell if the showers are usable now due to COVID. And until the end of AT lockdown (till 13/12) the lounges can only be used as waiting areas. Take away package when leaving the lounge.

The only possibility of a lounge access on arrival in VIE is going to the airport owned SKY Lounge - access with PP, Diners or AT issued Gold/Plat Amex and OS M&M black Mastercard.