Can generating a shapefile from a pgdb cause topology errors due to floating point conversion? I am running into gaps in a line layer of really small distances (order of 10^-4; CRS EPSG:2227 usft).
Shapefiles still store numbers using 64 bits of precision, 16-16 digits. It looks like you need 11 or 12, so you should not get errors unless you are doing computations in which case floating point errors are a remote possiblility.
If anything is ever converted into a 32-bit floating point number you would definitely lose precision.