Will Visio 2010 32bit work on MS Office 2013 64 bit .
From experience, even if you can get bits of 32-bit Office and 64-bit installed side-by-side, getting them to work together opens up a new world of pain. Why would you want to, anyway? If you have a license for 32-bit, surely you have one for 64-bit? I'd say that unless your users have H U G E spreadsheets - and let's face it, Excel's the only product in the suite that might need 64-bit - avoid.
Lastly, you're aware, of course, that MS explicitly counsels against installing 64-bit Office?