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Espruino is a JavaScript interpreter for low-power Microcontrollers. This site is both a support community for Espruino and a place to share what you are working on.
@Robin
Sat 2018.09.01
The only stupid questions are the ones not asked.
@Marty_McFly ambitious, aren't we!
While your intentions are admirable, checking the datasheet and the Pico specs will give you that answer. The following is the analysis process one should go through.
Datasheet
http://data.energizer.com/pdfs/cr2032.pdf
One can tell at a glance from the table that the voltage drops off considerably with higher current draw.
Device
As you also verified, and also under heading 'Battery'
http://www.espruino.com/Pico
Analysis
My understanding is that the Pico was to draw power from the USB port at 5v, and also stand alone LiPo battery 3.7v. In the design then, was a voltage regulator for the microcontroller, that also requires a slightly higher voltage in order to supply steady state 3.3V This then would require a supply voltage slightly more than 3.3v. That would prevent the CR2032 from being a power source choice. I think you realized that.
What other components do you intend to power at the same time?
Alternatives
Looking up Alkaline CR2032 now . . . .
EDIT
Lithium 3v and Alkaline seem to be available at 1.5v only
https://www.h-squared.co.uk/single-use-button-and-coin-cells