This thread is virtually pointless, north, unless you're going to define "dimension" first. If we take your "it would have to affect things if it ceased to exist" as a definition (and ignore the fact that to affect something implies some sort of causal link which requires an ordering of events which implies the existence of time) then obviously time meets that definition - how could you even imagine a universe without time, let alone claim that our universe would be unaffected by its absence - utterly ridiculous!
If, as I suspect, the definition you're actually thinking of is more along the lines of the wikipedia's first entry...
In common usage, a dimension (Latin, "measured out") is a parameter or measurement required to define the characteristics of an object—i.e. length, width, and height or size and shape. In mathematics, dimensions are the parameters required to describe the position and relevant characteristics of any object within a conceptual space/
...then you would be right that in Newtonian physics time isn't a dimension (by that defintion - it still could be called a dimension by a more general definition). But even if you're using that limited definition of dimension then either you are wrong or special relativity is wrong [ you don't need GR and expanding space to make this point ]. In Newtonain physics the distance between two points in 3D space (the metric) is agreed by all. In SR time and space are interwoven such that this is no longer true, but the distance between two events in spacetime (a 4 dimensional "space" that includes a time dimension) is - so to unambigously describe the extent of an object you need time as a dimension too.
If you're going to tell us that relativity is wrong you'd better have a better argument than some metaphysical musings about the non-existance of time.