No. It will work to detect any creatures that intrude the warded area by entering or touching it; this is not such a case though.
TL;DR - The spell is Alarm, not detect creature, nor detect life. However! Magic Mouth is the (2nd level) spell you're looking for to set up this sort of "scanner" in game as you can specify such a trigger "when within 30 feet of a mimic" etc.
As described, Alarm is a 1st Level spell with the following effects (emphasis mine):
You set an alarm against unwanted intrusion. Choose a door, a window, or an area within range that is no larger than a 20-foot cube. Until the spell ends, an alarm alerts you whenever a Tiny or larger creature touches or enters the warded area. When you cast the spell, you can designate creatures that won't set off the alarm. (Details on the type of alarm and triggered affects follow)
This includes invisible creatures, mimics, even creatures pretending to be objects (so long as they are still considered creatures) BUT only if they intrude via entering or touching the warded area.
If you ward a window or door, and someone touches the door after the alarm is set. Your alarm triggers as soon as they touch (or enter it if left open for some reason).
If you ward an area (20ft Cube) the alarm is triggered if a creature enters or touches the area (same as above).
So if I ward an area with statues already in it trying to see if one of them is a creature hiding in plain sight, will my alarm trigger from the creature touching the area?
This is where the debate is.
- Do native occupiers of the area considered, "touch" the area?
- Are they considered to be intruding?
Answer to 1. Technically they already were touching the area prior to the alarm being set, so "touching" the area they still are.
Is there a difference though between "first touching" and "already touching?" I believe so, example:
If you were to be advertised, "If you sign up now, we have a special offer!" and you explain, "I've been signed up this whole time, where's my special offer?" It isn't a surprise to find that there is a difference between establishing a new status, and continuing an already established status when they say no special for you. It would stand to clarify "is touching" or "first touches" but simply "touches" is ambiguous enough to look to context for clarification.
(Others too have mentioned, there is another unspecified difference between "the status of two things touching", and "the action of reaching out and touching something.")
Since this isn't clarified directly, we can look to the description for context to read the intention of the effect.
You set an alarm against unwanted intrusion.
So the alarm is specifically against "intrusion", defined as:
putting oneself deliberately into a place or situation where one is unwelcome or uninvited.
Which a non-moving, already in place creature that you approach is not doing. To intrude requires a state change of "out of area" to "in area" which these mimics would not be doing.
Further reasoning for the interpretation of intrusion:
Are my bones intruding my body? My bones are currently touching my muscles, my skin, and is indeed inside my body etc... but they would not be considered to be intruding."
So the Answer to Number 2 in the case of scanning for non-moving, hidden mimics; unless they move into (or are moved into) an alarmed area, intruding they are not.