I believe by design of the GC implementors, you can't speed up GC with nullification. I'm sure they'd prefer you not worry yourself with how/when GC runs -- treat it like this ubiquitous Being protecting and watching over and out for you...(bows head down, raises fist to the sky)...
Personally, I often explicitly set variables to null when I'm done with them as a form of self documentation. I don't declare, use, then set to null later -- I null immediately after they're no longer needed. I'm saying, explicitly, "I'm officially done with you...be gone..."
Is nullifying necessary in a GC'd language? No. Is it helpful for the GC? Maybe yes, maybe no, don't know for certain, by design I really can't control it, and regardless of today's answer with this version or that, future GC implementations could change the answer beyond my control. Plus if/when nulling is optimized out it's little more than a fancy comment if you will.
I figure if it makes my intent clearer to the next poor fool who follows in my footsteps, and if it "might" potentially help GC sometimes, then it's worth it to me. Mostly it makes me feel tidy and clear, and Mongo likes to feel tidy and clear. :)
I look at it like this: Programming languages exist to let people give other people an idea of intent and a compiler a job request of what to do -- the compiler converts that request into a different language (sometimes several) for a CPU -- the CPU(s) could give a hoot what language you used, your tab settings, comments, stylistic emphases, variable names, etc. -- a CPU's all about the bit stream that tells it what registers and opcodes and memory locations to twiddle. Many things written in code don't convert into what's consumed by the CPU in the sequence we specified. Our C, C++, C#, Lisp, Babel, assembler or whatever is theory rather than reality, written as a statement of work. What you see is not what you get, yes, even in assembler language.
I do understand the mindset of "unnecessary things" (like blank lines) "are nothing but noise and clutter up code." That was me earlier in my career; I totally get that. At this juncture I lean toward that which makes code clearer. It's not like I'm adding even 50 lines of "noise" to my programs -- it's a few lines here or there.
There are exceptions to any rule. In scenarios with volatile memory, static memory, race conditions, singletons, usage of "stale" data and all that kind of rot, that's different: you NEED to manage your own memory, locking and nullifying as apropos because the memory is not part of the GC'd Universe -- hopefully everyone understands that. The rest of the time with GC'd languages it's a matter of style rather than necessity or a guaranteed performance boost.
At the end of the day make sure you understand what is eligible for GC and what's not; lock, dispose, and nullify appropriately; wax on, wax off; breathe in, breathe out; and for everything else I say: If it feels good, do it. Your mileage may vary...as it should...