Any speculation on the effects of any human related behavior, like tiredness, are just that, pure speculation. we have the illusion to have enough knowledge about these things to infer conclusions and emit opinions about it but the truth is , we don't even know what we don't know. There are inumerous processes that we don't grasp yet the full scope and spectrum of their consequences and side-effects, much less the ones we are yet to discover.

In relation to tiredness, specifically, it seems to me that it's an evolutionary trait that involves all sorts of chemical responses from the body, besides the related induced brain activity, This works to save energy and to ensure it's spent on activities that benefit the spread of the genes, somehow. You get tired mentally (what you are specifically referring to) because the executive function of the brain taken by the frontal-cortex are the most energy expensive one and gets shut-off as soon as anything that can be perceived as life-threatning is detected so that energy can be redirected to the fight-or-flight response required for your survival, as it's coded in your genes.

Now, assuming it will be possible, an uploaded version of whatever human conscience there could be, it would not need to have any of these energy regulation stuff. Or at least as much as we need it right now, as humans, per the limitation by our body's capacity of energy intake. The uploaded conscience would have at its disposal an quasi-unlimited amount of energy to it would not trigger the tiredness response or any "suffering" reflex.

However, of course, I really don't know ;)