I think I read of someone doing it in UB a year or two ago.
RUS Transit Visas are primarily intended for journeys starting and ending outside RUS and being in RUS is an unavoidable side-effect. Like being on a train that crosses into then out off Russian territories (even without scheduled stops), or flight stops/aircraft changes in RUS.
They are generally for up to 3 days duration only.
But they can be used for road journeys for periods on a calculation of a daily distance allowance based on the shortest distance between the stated Entry and Exit points. The period is based on a MINIMUM of 500km/day (312.5miles)
I would think they would take as long (or short) to process as other applications.
You could 'get a feel' for these here Russia Visa Information - UK - All About Your Visas - Transit
This is the London service - conditions and Documents required may vary elsewhere.
Note: Visa documents vary for differing nationalities but the UK site is fairly 'active' in this respect. The Embassy consular service has similar 'active' website/agents in other countries, but not all.