Not really! I use an XCompose file derived from the Plan 9 keyboard setup. So to write ∏ i press my modifer (left shift) button once, and then 'p' followed by 'r'. So it is fewer key presses than \prod (three key presses vs five).

I have similar shortcuts for all maths symbols I use regularly. Here is an excerp from the configuration

2200 fa ∀ for all

2202 pd ∂ partial differential

2203 te ∃ there exists

2205 es ∅ empty set

2206 De ∆ increment

2207 gr ∇ nabla

2208 mo ∈ element of

(…)

220E qed ∎ tombstone

The last one is most sattisfying to type !