What are the odds of alar rim grafts not working for first rhinoplasty? (photo)

Your columella needs no work, your surgeon knows well his work; your alar rims are retracted and there is the main focus to treat your exposed columella
However, regarding your fear, you are right, not performing an aggressive and solid re-supporting of the nostrils leads to failure, lowering your alar rims can't be done by merely using rim grafts; for example and based on the limited image posted, you have lateral crura malpositioning, probably a parenthesis tip deformity, and this needs lateral crura repositioning + strut o batten grafting on them + caudal extension grafts of the lateral cruras. Additionally your tip is poorly supported and you suffer the so called "tension nose" deformity.In short: a well done, strong and full blown structure rhinoplasty is a time stable solution for you; seek an expert in such field.
See the link below to find few cases of my own practice very similar to yours which I had the opportunity to operate successfully on, sharing a lot of common features with the technical problem you have posted.
If you wish better grounded opinion well lit, focused and standard images have to be assessed: frontal, both lateral and both oblique views, also underneath the nostrils.
Feel free to request any additional information from me.

Alar rim grafts are used to treat notched or retracted nostril rims. The decision to use them depends on analysis of nasal measurements specifically the distance between the rims and the mid-axis of the nostril plane vs. that between the outer edge of the columella and the mid-axis. In your photo the later is much greater so it is likely you would benefit from trimming of the septal cartilage at the bottom, which would either negate the need for or allow placement of a smaller rim graft.

Alar retraction occurs due to lack of cartilage support of the alar rim when excessive reduction is performed.  Replacing cartilage grafts either to the rim or to the tip cartilages helps restore the integrity to the tip and correct retraction.  Relapse is possible but unlikely.  In the photo, a combination of alar retraction and columellar show needs to be corrected. 

Hello and thank you for your question. Based on your
photograph, you may benefit from a combination of both lifting your columella and lowering your alar rims with an alar batten graft.  Make sure you specifically look at
before and after pictures of real patients who have had this surgery performed
by your surgeon and not just a computer animation system.
The most important aspect is to find a surgeon you are comfortable with. I
recommend that you seek consultation with a qualified board-certified plastic
surgeon who can evaluate you in person.
Best wishes and good luck.
Richard G. Reish, M.D. FACS
Harvard-trained plastic surgeon

 The limited photograph demonstrates significant columellar show, therefore a columella plasty would be helpful first, before using alar rim grafts. A columella-plasty involves removal of excess skin and cartilage in that area in order to tuck the columella upwards and inwards. For many examples, please see the link and the video below