If I have a cylindrical pipe, closed at one end, fill it with water and freeze it, will the ice burst the pipe?

This depends on the dimensions of the pipe as the open end’s surface area must allow a rate of flow that balances the surface area of the ice. This is related to the length and diameter compounded by the constantly changing(decreasing) volume of water to ice, but trending to freeze conically. All the while the escape hole decreases in area and if it closes and then thickens can burst the pipe but if open til nearly the end will allow escape of expanding ice and prevent pressures to burst a pipe. All this is also dependent on the material of the pipe as thermal conductivity and tension/compression/ shear limits. Generally, the pipe wall will transfer heat faster than the opening. Gas is less dense than a solid so, the pipe wall’s greater thermal mass will expedite ice growth. Also consider, ice molecules align rigidly to their hydrogen bonds and hold a crystal form with a lighter volume than liquid water’s fleeting H-bonds, so, ice will grow top-down as well. The H2O will flow on a path of least resistance so if the pipe wall offers less force than the ice’s path in and up it’ll burst through.

A few variables affecting burstage: pipe dimensions (aperture:length), material density and continuity, gas pressure and circulation on open end, rate ice freezes as frozen area and liquid volume change, decreasing aperture of open end, rate of expulsion of liquid water through opening, thickness of any enclosing layer of ice at opening, fluctuating water circulation, quantum fluctuations, etc.

You need a lot of calculus to make a decent model for predicting what would happen. In general, a stout pipe resists bursting and a scrawny one embraces a burst. Hopefully you see the relation between surface area of opening, surface area of freezing ice, where the ice forms and that liquid and ice flow toward area of least resistance, and the various dimensional factors at play.