Is it possible to amplify every single piece of DNA through PCR?
In short; Theoretically yes.

In practicallity no.

Non-specific PCR require random primers to anneal to a target sequence to initiate replication during PCR. Theoretically this should anneal to every combination of bases and therefore allow the amplification of all DNA (or at least in a fragmented form).

Practically, all the primer combinations will have different primer annealling temperatures due to the differential base composition, making the amplification of fragmentation inconsistent, and in others down-right impossible.