Email on Samsung Galaxy Reverb

If I download my emails form my main computer and then walk over to my 2nd computer I will get about 10% of my emails from the last 10 days, don't know why but not of them had attachments.
So my question is if someone sends me 20 megs of pictures and I just happened to be at the doctors office at that time am I going to get those 20 megs of pictures on my cell phone? Downloading
20 megs on my computer only takes seconds but on my cell phone it would be a nightmare.

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As long as you setup the e-mail as IMAP the messages will be available in all locations.