My baby also 邊食邊訓. although he is sleeping, he can still suck and get the milk. Of course, the sucking motion will not be continously and there will be some 'pause' between.
for breastfeeding baby below 6 months, please do not give them water, as it will affect your milk supply because their stomach is too small, it will delay asking for milk.
also, breastmilk contains 87% of water, it is no need to give them water.
i also heard from the doctor /web info, their kidney cannot afford too much water. please note.