No, someone asked this the other day. Send Alert is based on Lead, not Owner.
If you have the same alert, you can do Run Once a Day to reduce some of the Alerts. The best thing is to adjust your process.
Chelsie, not just one but 2 recent threads on essentially the same topic:
As Josh notes and as you can see in those threads, throttling alerts is only possible if you use a webhook to maintain a counter (i.e. to only send to each sales rep 3x per hour, or 3x per day per Company, etc.). This works by simply ignoring any alerts that come in after the quota is exceeded.
But even this kind of throttling, which is relatively easy to implement, can't accomplish the concept of an "alert digest" -- that is, one email that rolls up all the updates in a given time period. The reason it can't do this is pretty logical: if everything is triggered, then when the day's first alert comes through, the system would have no way of knowing there will be a second alert. It has to send the first alert as it comes in.
You can use custom development to generate alert digests, but only if it's worth the expense.