Technically NO. This is because it is not their baggage.
But, there is a lot going on here so there is no way to definitely answer this question.
If you miss the connection, it is possible/probable, though not always required, that your luggage be unloaded from the flight.*
Alternatively, depending on the airline and attentiveness of baggage service at the destination, if your bags do go ahead of you, they may be send directly to storage instead of the carousel.
In that case, it may depend on the discretion of whoever is staffing the luggage desk. Maybe your spouse can collect them, maybe not.
*For the nitpickers, there are different rules for irregular situations though today, airlines do a much better job of keeping baggage with the passenger and will prefer to offload. This is because it's much easier to locate bags now and baggage going ahead is a different scenario than lost/delayed baggage.