No literal part-time statutory status, but de facto part-time can be attained. It depends on the specific work contracts, which vary airline to airline. Some are more poised than others to empower a junior or middle of the road seniority guy to be able to drop or give away flying with any level of consistency. Senior guys of course are not germane to this discussion. If we could all be senior from day one this wouldn't be a question.
In general, given the median mainline pilot is a primary-payer type, an overstaffed airline is much more prime for a min runner type to be able to give away trips (basically a form of trade), since your peers are chomping at the bit to grab any additional work left on the table. Assuming the work rules are there to allow it of course. Ditto for those airlines which have work rules that allow straight dropping to X credit (even zero credit), provided that there is coverage (again, overstaffing is stipulated). This also further depends on the actual base, seat and equipment, which itself has differing staffing levels intra-airline.
IOW, too many factors to say for sure, and staffing levels unfortunately fluctuate, so it's a moving target. I suppose the most reliable way to predict the viability of min-running, is asking about the work rules regarding trip drop or trip giveback/away to the company, and of course, staffing levels.