Simple Answer:

No.

More Explanations:

Faster Cutting?

Chrome does not help to reflect the heat back at metal to increase cutting speed. With something as small as a cutting tip, only the direct flames are hot enough to heat metal.

Think about this: Would a cutting tip be sufficient to cover a pot on a stove to heat food faster? Of course not, so there's no way that a cutting tip can reflect enough heat to help cut metal faster than the direct flames alone.

Less Dirty?

Chrome does not help to keep slag, chili, dirt or otherwise stick any less to cutting tips.

More Shiny?

Yes, chrome is perfect for making cutting tips look shinier and fancier. Unfortunately, this does not help to increase productivity... unless shiny cutting tips make operators happier and therefore more productive.

What could chrome plating possibly do otherwise?

If your facility uses both acetylene and alternative fuel gas cutting torches, then having non-plated acetylene tips and chrome-plated alternative fuel gas tips can help to easily distinguish the two types.