I sit here and chuckle at the question. Not at you but because the answer is best found out by having the parts in front of you or from someone who has the case. Side fans are usually 25mm wide. I checked a few places (even Cooler Master's website) and no where do they confirm the fan's thickness in the specifications. As for the motherboard side of things, there is more than just the motherboard to consider. First the board itself is ~2mm thick. The height of the CPU from the board (5mm?). There are also the motherboard standoffs (~5-7mm) and the motherboard tray (~1mm) to consider. So far we are up to 13-15mm but there is one more point to consider, the spacing between it and the left side panel. The answer to this lies with the case itself because it is a spec that I have never seen listed. Let's take the information we have so far and do the next best thing - guesstimate. The cooler is 160mm tall, side fan is 25mm, plus the 13-15mm = 198-200mm. If the case is only 213mm wide (minus 2mm for the thickness of the side panels = 211mm) this leaves 11-13mm left. So if the space between the motherboard tray and the left side panel is smaller than this then the cooler will fit. If it is larger then the cooler will interfere with the cooler and you would have to take the fan off for it to fit. Do you see why I chuckle?
Yes I do.
Will getting rid of the fan really change much if I add another elsewhere?
Can I be pretty sure that it will fit with the fan removed?
11-13mm... for the average case, would I be allright?
Depends on the side fan. 120mm fans are usually 25mm thick, but the larger 200-360mm fans can be hit 40mm thick pretty easily. And even if the case is 210mm wide, you're not going to get all of that, because some of that width is taken up the back panel, the space between that panel and the motherboard tray, the motherboard standoffs, the CPU socket on the motherboard... but as said above, if the case is designed well, you can just ditch the side fan without loosing too much cooling.
i7 2600K | ASUS Maximus IV GENE-Z | GTX Titan | Corsair DDR3-2133