Great Question: Can Time and Position affect your GPS accuracy.
Short Answer: YES
First lets place your GPS Receiver in perfect conditions where the atmospheric conditions are perfect, there are no multipath effects, no radio interference, and line of sight to GPS Satellites is clear.
Your Time and Position on Earth will determine where the GPS satellites will be in relation to you. Relative to your earth postion, the GPS satellites have their own positions that will give you a maximum accuracy and precision GPS Location. Any deviation from this theoretically perfect alignment between you and the GPS satellites will degrade accuracy to a point where no accurate position can be computed.
Besides the Windows Tools provided by other very helpfulls, I really love the NAVCOM online website tool for quickly checking GPS satellite availability and predictive DOP in TIME relative to co-ordinates given.
NAVCOM GPS Satellite Predictor Tool
Great tool if you require a certain level of (x)DOP for GPS Data Collection, to prevent spending an entire day in the field due to poor (x)DOP of GPS Satellites. Of course this tool can not calculate other external factors which will affect (x)DOP.