Yes, as everyone needs negotiation skills, tester or not.
When we say we need 4 weeks to test a new piece of software to the extent we will be happy and covered what we want, and they only want you to have 1 week, you have started to negotiate.
Do you blindly accept you only have 1 week?
Do you make your case for why you need 4 weeks?
Can you compromise and meet in the middle?
Can you get the time down with more people helping out?
We are always after more time, more people, more resources (soft/hardware, as people aren’t resources), and if we can’t make our case as to why we need them, we will get treated poorly.
But we also need to understand their side, as if we won’t listen, we are simply stubborn children who won’t back down, even if there is a good reason.
Also, with any question like this, I always flip it and ask “Why shouldn’t testers learn to negotiate?”