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Can a Sergeant armed with a powerfist elect not to use it (and therefore, strike at initiative) in close combat?

No, he is forced to use it.
You could do that in old editions, but not in 5th.

The rule in question can be found on page 42, under the Subheading "A normal and a special weapon":

Page 42 wrote: A normal and a special weapon
These models gain one additional attack. All of their attacks, including the bonus attack, benefit from the special weapon's bonuses.

Red for Emphasis. As you can see, all his attacks must be done with the Special Weapon. He cannot elect to use the Normal Weapon Instead or not use it at all.

Edits: [Jedi]These are not the Droids you are looking for[/Jedi]

Actually that's not the rule you're looking for. There is a rule that says you must use any special attacks that you have. I'm away from my rulebooks right now but I'm sure someone will post the appropriate passage.

Page 35, third paragraph.

logan007 wrote:Can a Sergeant armed with a powerfist elect not to use it (and therefore, strike at initiative) in close combat?

If you gave him a power sword and a power fist, you could elect one or the other. As Gwar stated though, you must use your power fist on INT one if you don't have a power sword to use instead.

This is why Magnus Calgar has a Power Sword, and A Power Fist in the new SM codex.

And one hell of an attitude to boot .