Depends what sort of infection it is.
If the infection on the hardrive (which is being connected in a way an external data storage device generally would be) is not active, and is just within some of the files then others should be safe and infection fre, and for the host machine to be infected a use would need to run one of the infected files on the HDD.
If the infection on the hard-drive has some sort of autorun system which lets it execute automatically as soon as connected to any device then the host will get infected.
It all depends on the type of infection. Best NOT to try anything like this unless you can be utterly sure the infection is of the first type and that it isn't in any of the files you might want to copy from the HDD.
You might consider plugging the HDD into a machine running a linux operating system, then copying off anything you need to (don't copy off exe, scr or dll files, assume them to all be infected), then using that machine to format the hard drive. If copying off any files you will need to scan them heavily, there are tools which can be run on a linux system to check files for infections which might become active if they were opened on a windows system.
Regarding autorun, some types of auto-rnning are still possible aren't they? In general it isn't but at present there do exist viruses which can write themselevs to USB and then infect any machine they are plugged into without the user needing to delibrately open any files on the USB. There have also been some discoveries of problems within the USB type of connection itself which could be used to put viruses into the firmware of a USB, the principles might be different to traditional autorun but the end result is similar.
Edited by rp88, 19 May 2015 - 12:09 PM.
Back on this site, for a while anyway, been so busy the last year.
My systems:2 laptops, intel i3 processors, windows 8.1 installed on the hard-drive and linux mint 17.3 MATE installed to USB