Indeed it is as SDS/PAGE is the only analytical technique which allows you to visualize the quality of the samples. This quality control is necessary to select the richest and purest fractions.
Well... it sounds like if that question comes up at all, the answer would almost certainly be yes. If you're doing a purification for the first time, things do not usually go the way you imagine. You need to learn in what fractions your protein ended up, and what else ended up in those fractions. There is often not a good way to predict this, and so you need to look, by gel.
Once you've done a process successfully start to finish a number of times, and feel very experienced with it, and it does in fact behave consistently every time you do it, you can think about cutting corners. (omitting some intermediate gel steps and taking the results "on faith". The worst that can happen is that you don't get your protein in the end, so you can bet some of your time that things will be OK at your own discretion. But stay away from this while you don't feel very confident.
yes indeed ,it is important to see outcome of your results and make your discussion for next steps. I think it is rather checking your work also saving the time and cost of your next experiment.