No — a search alarm sends nothing. Despite the name it is a saved search, not an alert: no email, no in-app notification and no push message is produced when a demand matching it is published.
So the alarm does not come to you; you go to it. Open Marketplace, click your saved alarm, and the filters you froze come back in one tap with everything published right now listed under them. The value is the saved setup, not the watching — checking your alarms is a habit you keep, and nothing will remind you to.
There is no setting that changes this. The toggles under Settings › Notifications cover New offer, Message and Demand status only; no "a new demand matches my alarm" option exists in that list, so there is nothing to switch on.
Two things do work in your favour. Saved alarms live on your account rather than in one browser, so they are waiting when you sign in from another device. And if you rely on a category rather than a search, widening the categories on your company profile brings more demands into the Marketplace list itself.
Also asked as: Does a search alarm send email? · Will I be told when a new matching demand is posted? · Does a saved search alert me? · How do I turn on alarm notifications?