Yes a mini-pump will inflate a 23 or 25 tire to moderate pressure but takes 200 or more strokes to get there and, unless you have a road Morph or one of the Lezyne pumps with a hose connection, you stand a decent chance of snapping off the valve stem.

I carry both a mini-pump and a couple of 12 gm CO2 cartridges. I use the mini-pump to get the newly installed tube to 25 or so psi which makes sure it's seated right and holds air. Then one CO2 cartridge gets the tire to about 100 psi which is fine. Modest pumping time and full pressure without the endless strokes of the pump alone. The combination weighs significantly less than an HPX I used to carry and 12 gm unthreaded CO2 cartridges are very cheap if bought at a big box store.