I need to make a poster to present at a conference and I'm wondering if there's anyway to do this all in ArcGIS 10.1.
Is it possible to change the layout/page size to 36x72 inches?
Is it possible? Sure, just create a new document at any size (doesn't matter), then click File->Page and Print Setup and set the width and height to whatever you want.
As to whether this is practical, I can't say since I don't know what you're trying to do. The complexity of the map depends on the content, not the sheet size, at least until you try to export the whole thing as a jpg at 300dpi, or some equivalent bad idea. Even then, it's just a matter of how long your willing to wait for the export and how much disk space it will consume.