Any modal message—full-screen or alert—that interrupts user flow to ask them to download your app suffers from #doorslam an ux antipattern.
See some examples here: http://idontwantyourfuckingapp.tumblr.com/
Promotions should never steel the show. If you present your users a full-scale layover as the first thing they see if they visit your site, you can be sure that you will annoy them. Most likely you will especially annoy your most loyal and familiar customers.
Users will come to your site to do some task and they don’t like anything that gets in their way. It is even more suprising that companies add such a ux anti pattern although they have a mobile optimized site.
You should never loose the opportunity to engage with your users.
Customers will tolerate a dismissible banner if it doesn’t take up to much space on the screen.
So please stop ruin’ the mobile web! Thanks!