Can Roku do this?

It isn't really clear from what you posted exactly what you are trying to accomplish. Do you want a Roku screen that updates every few minutes? Do you want an image that updates every few minutes? As you probably know, a Roku can't really display a web (html) page. Instead, the Roku can take XML data and render that in many different ways. To do something on a timer, one can easily create a timer and perform an action on a regular schedule:

timer=createobject("rotimespan")
timer.mark()

while true
     if timer.totalseconds() > 60 then 
          doMyThing()
          timer.mark()
     end if
end while

If the server is providing data to the webpage, it should be able to provide data to the Roku as well. You'll probably need the following bits to get this working.

1. Create a timer loop as jbrave mentioned above.
2. Query your server for the data that forms the webpage (XML/images are likely preferred format).
3. Parse the data from the server and render it using BrightScript tools.

As jbrave mentioned, the Roku does not support directly rendering a web page to the screen. You'll need to write your own functionality to display out the contents.