Eh? That rather depends on the mini-pump.
And if you were running such sealant in a high pressure tube most of it would be forced out of the hole (making an almighty mess of the inside of the tyre in the process) before it reached the lower pressure at which it could function. Which means that you'd have to carry it with you to install post-puncture.
I'd rather carry a spare tube as a 'get-me-home fix' than a tube of low pressure sealant.
The Holts Tyre Weld stuff doesn't inflate the tyre, a small quantity of propellant is provided just to help pump the sealant into relatively larger car tyres. You squirt it into the inner tube, spin the wheel (with the still-deflated tyre on it) so it distributes itself all over the inside of the inner tube, THEN pump it up, hoping it seals the puncture while you are pumping. It never sees high pressure unless you go mad with the minipump.
I have heard it outperforms Slime as a sealant, which from my experience won't be difficult
but it has the advantage that it doesn't have to stay chemically stable inside an inner tube for months or years before it gets called into action.
Me? I'm a patch man, myself.