I have had a smart phone for many many years, way before many had them (I had the original Palm phone), and I can say honestly, its really not a hassle to read emails on them, at least for me. Even if they are long.
And honestly, responding really isn't much of a hassle either. I do tend to keep things brief, but I never use text speak - smart phones have full keyboards and email programs don't have character limits like texting. Anyone choosing to use improvised spelling and bad grammar is doing just that choosing to use those things. Its not a limitation of the device they are on, its a limitation to their realization of how unprofessional those actions are.
Your agent told you emailing is fine, so feel free to email.
But you do specifically mention "long emails" - honestly no matter what they are reading on, computer or device, editing is always a your friend in writing. Try to keep things as brief as possible - if its not possible to go less then a full page of text, so be it, but don't do a full page of text when one paragraph and 8 bullet points could have worked just as well. Humans, in general, respond better to lots of white space and less text on a page.