Yes and it's nowhere near 600W, heatpipes are no go because their working principle depends on temperature differential, which you can't have. Power consumption might be 600W, yeah.
100W of cooling power is realistic with what is shown. Given enough time and thermal insulation, that of course can freeze water, concentrated into such small volume.
I did build a fairly successful Peltier-based cooling device which I use to calibrate sensors. 6 * 60W elements mounted to a totally massive heatsink with large radial server fans. I can successfully freeze water with it, but this also relies on room temperature being just 20degC or so. Make it 30 and you are out of luck.
But anyway, this is no rocket science. Basic thermal calculations work. Look up the datasheet, typical performance is 100% COP at dT=0 linearly down to 0% COP at dT=55degC.
What this means is, if both hot and cool sides are at +20degC, you consume 100W of power, cool at 100W, and dissipate 200W of heat. Obviously dissipating 200W means temperature differential RthJ-A * 200W over the hot side alone, making the hot side not +20degC, but maybe +30degC with heroic cooling efforts. With dT=10, COP is already down to around 80%. Which means we are at equilibrium, consuming 100W, cooling 80W, and dissipating 180W.
Now the water slowly cools down, and when it's at 0degC, dT is already 30degC - still assuming air-conditioned 20degC room! - and COP is down to maybe 40%. Power in = 100W, cooling = 40W, heating = 140W.
Latent heat required to freeze water is massive, so with just 40W, it takes forever, but eventually it will happen, of course. At that point, you have dissipated so much energy that the room has likely heated up.
But sure, if you have good air conditioning, turn that as low as possible to keep the room cool, and you have chances of success. Say, if you buy 1500-2000W nominal of Peltiers, derate them to run at say, 1000W, use a car engine radiator block with a massive fan to liquid cool the peltiers, and have that radiator inside an air-conditioned space (or only do ice cream during winter), it likely works out.
Easier solution: get a used freezer, and build the ice cream maker inside of it.