Time-memory tradeoffs in Shor's algorithm

Can a quantum computer with insufficient qubits to factor an integer of a given size make any progress in factoring it? For example, what if a quantum computer is only one qubit short of what is necessary to attack a specific integer? Is it capable of making any progress in factoring it, or would it be just as useless as a 2 qubit machine? Assume qubits refer to logical qubits in a general-purpose cryptanalytic quantum computer with sufficient quantum error correction to solve the problem of decoherence.

Given that qubits can be thought of as the memory for quantum computers, I am essentially asking if time-memory tradeoffs are possible with Shor’s algorithm when too few qubits are available.