Short and Sweet: YES, do take the time to clean your electronics. Below is my own subjective experience. YMMV
When I was 17 I owned what was arguably the best laptop available to consumers in the whole world. It had the first edition of Pentium 4 mobile processors, a dvd burner and a 32 MEG (!) GeForce 4 mobile video card. I was the envy of all my friends. (I got it from the make a wish foundation after having cancer, they envied the laptop, not the cancer)
A year later the CD drive seemed to stop reading any media that I put in. It was intermittent for a long time but eventually it wasn't able to read anything. This made was a pain because bios' back then didn't support booting from USB and when I wanted to re ghost the thing the CD's were useless. I tried booting it over the network but that was a huge pain in the ass and didn't go well. I continued to use the laptop for another year or two.
I got a new desktop computer and the laptop went to collect dust in my desk drawer. A few years later I was cleaning out my desk and brought out the old laptop, wondering if I could get the OS reinstalled somehow. CD ROM drive still didn't work. I took a Q-tip and swabbed the little laser lens thingymabob just for shits (it didn't look dusty or dirty) Magically, Every CD I put in suddenly worked. The lens was just a little smudged I guess. I didn't use a perfectly good computer for years because of some stupid dust. (I forgot to mention, the computer was at a point where I reformatted but hadn't put any os on it so it was useless even for simple tasks)
I also had a desktop computer that use to freeze occasionally during times of intense rendering / cpu usage. It was pretty old and when I opened the case there was a lot of dust collected in the proc's cooling fan. I just blew on it (no canned air) and got most of the dust out. No more over heating problems.
Keep your boss's boss off your boss's back.