From what I have seen in different places, Thomas Sprigg (c.1630-1794) was the son of Thomas Sprigg (1604-1678) and his wife Katherine Griffin (c. 1610, d. aft 1667, in Maryland). Katherine is said to have been the daughter of George Griffin of Kettering, Northants, England, who was born in 1594.
There used to be an excellent and well researched web site on the Sprigg family, which was created by a Professor Marler; but I am afraid I cannot find it anymore. I did a computer search and found the following sites... The first one mentions your Alice, but doesn't come to any definite conclusions about her, other than to say they don't think she was the daughter of the Thomas Sprigg who was born 1630.