So this is why my smartwatch can tell me my speed before it has a GPS lock, including indoors? Very cool! But of course, as you say, the reports of my absolute position are very inaccurate.
Velocity can come from dopplar shift of the GPS carrier frequencies. This is very accurate. An IMU can be used for walking speed estimation but it won't be as accurate using a human gait model or direct integration.
No, any position-solution produced before a GPS lock will be due to the approximation produced by either using the last-known position or the cell-tower triangulation.
That information is also used as a seed for the GPS lock to speed up the time-to-fix.