Do you mean store the picture's file address as text in an SQLite database? That shouldn't be a problem.
As for the memory, it depends on how many pictures are being stored. Modern devices have tons of storage space and modern users tend to store tons of pictures and video on their devices so it wouldn't be out of character for those. Older devices will have less storage space and their users might not take kindly to what little space they have being unnecessarily hogged by a single app. I would check for how much storage space they have and store pictures accordingly.