No, organic livestock may not be managed under non-organic circumstances, even if that management is only temporary.
The National Organic Program (NOP) has very specific organic livestock origin requirements in place to begin with and once you've got organic livestock they must remain under continuous organic management for their lifetime. You may not transition organic livestock back and fourth between organic and conventional management.
NOP policy (§ 205.236) states that any currently organic livestock or edible organic livestock products that are removed from an organic operation and subsequently managed on a nonorganic operation may no longer be labeled, sold or even represented as organically produced.
A common situation in which transfer of livestock occurs is when dairy farmers send their young cows to a different farm until they come of milking age. For an organic producer, care must be taken in situations such as this to make sure your cows are under continuous organic management. However, note that cows aren't the only livestock this rule applies to. No matter the animal, what goes organic must stay organic in order to reap the benefits organic certification affords you.