Modern tape transports are locked to digital crystals, and are extremely stable. As a digital audio system, your Digi 001 or ToolBox system has an extremely stable crystal oscillator. When your Pro Tools LE-equipped system triggers to the incoming time code from your tape deck, the systems will stay locked for pretty long periods of time (even minutes). For example, triggering to MTC generated by an ADAT (maybe using the BRC or a JL Cooper DataSync2), you're likely to be able to lock to a 5 minute tune with no significant drift, because of the relative stability of the transports.