Getting one kW out of a 1.5v battery would require a fairly huge current (>600A), and the cabling and motor design would be equally huge.
Ignoring the infeasibility of that part of the design, very few chemical batteries can produce that sort of current, certainly no off the shelf battery designs.
You may be able to get a moderate boost over a longer period of time, and as others have said stuffing the frame with batteries of a very modern battery types (eg Lithium Polymer) might work, but as Roger points out, converting that into a usable torque at the bottom bracket would be challenging.
It does strike me that if this is considered a potential problem, then checking bikes for it would be trivial, if their excessive mass doesn't give them away, a quick X-Ray certainly will, this will be a complex and easily identifiable structure.