Well yes, Benzo's would offset the alcohol withdrawal symptoms, because Benzo's act as agonists on the same receptor sites as Alcohol. But because of this, the Benzo's can kick start a fresh new cycle of withdrawal, very similar to alcohol withdrawal, but with increasing severity.
There's a reason why people trying to kick their alcohol addiction are only prescribed Benzodiazepine's for a very short period of time. Using them beyond a certain time frame can lead to more severe withdrawal symptoms, either leading to Benzodiazepine dependency or Alcohol relapse to combat the worsening withdrawal symptoms.
0.5mgs of Alprazolam may not seem like much. But it's still equivalent to approximately 7.5-10mgs of Diazepam. Not only that, but it's very short acting compared to Diazepam, it's absorbed into the blood stream more quickly and reaches the nervous system more quickly, making it more potent.
When I was using Alprazolam and Diazepam, I was only occasionally using similar doses to yourself and for a long while I felt fine. Then one day I was laying on the couch and my heart rate suddenly shot through the roof and I felt like I was about to die. I had no choice but to reach for the Benzo to calm my nervous system back down. This started the worst several months of my life where I felt like I was in an endless panic attack. I had to taper extremely carefully, all the way down to just 0.5mgs of Diazepam. Even once I finally broke free of them, I still had severe insomnia (only sleeping about 3 hours per week), my arms and legs wouldn't stop twitching. I developed black spots in my line of vision (presumably due to damage to neurons connected to my visual cortex, likely due to the influx of Glutamate) and had severe tinnitus in both ears.
I'm doing much better now a year on, but my eye sight still hasn't completely turned to normal and perhaps never will and I still have moderate tinnitus in my right ear.
This all occurred after months of feeling absolutely fine with occasional low dose Benzo usage, then suddenly not feeling fine one day.
When I say that Benzodiazepine's aren't quite like any other drug, I literally mean it. The withdrawal can either creep up on you over time, or it can just instantly hit you at any point in time without any warning at all.