Can a Non-Thunderbolt device (like a mid 2010 iMac) connect to a Thunderbolt Display?
No, it cannot. That's the reason Apple is still selling the non-thunderbolt 27" display, for the devices like yours.

Source: Apple Online Store, where under system requirements it says:

System Requirements

Thunderbolt-enabled Mac computer, including MacBook Air, MacBook Pro, Mac mini, and iMac