Will the absence of connected charger increase the cycle count? I'm a new MacBook user, so I may be relying on rumours instead of fact.

It sounds quite silly, but, from my perspective, if I always hold my laptop connected to a charger, then my battery is always around 100% and it seems like the battery cycle count is not growing at that time. And, if I take my laptop somewhere without a charger, then I get this 40-60% decrease, then I think it's at this moment the cycle count increases more than it would if it is connected to a charger.

I guess I'm a little confused by cycle counts. What are the facts about how they are measured?
I'm not entirely sure I understand your question, but one cycle is equivalent to a full discharge then recharge.

So, using your example, if you use the MacBook without a charger and its charge decreases by 40% and then you recharge it, that's effectively .4 of a cycle. 

In other words, to use a simpler scenario, if you use half of your MacBook's charge in one day, and then recharge it fully, and then the next day you do exactly the same, those two days combined would count as one charge cycle.

So, some users may go through a cycle a day, others can use their MacBook for weeks before completing a cycle.

For more info on this refer to Determining battery cycle count for Mac notebooks.