Yes, you can perform Umrah while on a visit eVisa.
From the official eVisa website:
8.7 An eVisa is granted solely for tourist purposes or for the purpose of performing a umrah and it is not considered a visa for work. If you are granted an eVisa, you must not take up paid employment during your visit to KSA.
An extreme option is to convert to Islam (which only requires reciting the Shahada), receive a certificate of faith from your local mosque and then travel to Mecca as part of an Umrah pilgrimage. Andrei Markelov from Russia went for this route recently and published a long blog post about his journey to Mecca and Medina.
Of course, this should only be done ...