There's no reason they wouldn't patronize the online version for the right deal.
From the techcrunch.com
How nice it is to patronize and visit with our neighbors who own the shops there.
From the tennessean.com
Do you feel they patronize you and look at you as someone their daughter's age?
From the online.wsj.com
Would I continue to patronize a store if the owner's posts were unduly polemical?
From the psychcentral.com
Didn't you say how you're not going to patronize the site anymore because Kosovo?
From the economist.com
Don't patronize me, I am almost surely senior to you and have a better education.
From the economist.com
Diners feel good when they patronize a restaurant that promotes values they share.
From the democratandchronicle.com
For instance, they check in from a distance, only pretending to patronize a venue.
From the cnn.com
A note on the door asks customers to patronize the Altamont Avenue Friendly's.
From the timesunion.com
More examples
Sponsor: assume sponsorship of
Do one's shopping at; do business with; be a customer or client of
Treat condescendingly
(patronized) having patronage or clients; "street full of flourishing well-patronized shops"
(patronizing) arch: (used of behavior or attitude) characteristic of those who treat others with condescension
To make a patron; To assume a tone of unjustified superiority; to talk down to; to treat condescendingly; To make oneself a customer of a business, especially a regular customer
(patronization) patronizing behaviour or talk
(patronizing) offensive condescending
(patronized) (1) LOOK-DOWN-ON"th" pointed to self. (2) [B] strokes side of head.