S60v3 (E Series, N Series, 3250, 5700 etc) - Yes.
S40v3 (6300,5200,5300 etc) - No
If you have any S60v3 phone, then they can be minimized. Just press the menu key, and the Web Browser goes in background. You can access it again by keeping the meny key pressed, it will show the open apps. Select the browser and you can use it again.
If you are using S40v3 phones, then no. The browser cannot be minimized, it is not a multi tasking OS.