In theory - yes. However so little is known regarding the functional element(s) of a probiotic that the target genes to be modified or inserted would be an educated guess.
I'll also note that many marketed probiotic" products are pretty useless.
Article Identification of Bacillus species: Implication on the quali...
Phil Geis Number of doctors recently prescribed these probiotics for alteration of drug treatment.
There is some evidence to suggest that probiotics can enhance immune function by promoting the growth of beneficial bacteria in the gut. This may be particularly relevant in preventing infections in certain populations, such as children or the elderly.
and recent work is also going on Gut - Brain Axis.