Can having a valve too short cause punctures?
Short answer: Probably not.

Long answer: While it is technically possible to construct, a scenario, where a tube with a presta valve would get damaged,because the valve is too short/the rim is too deep, in my opinion it is highly unlikely that this is what's causing the problem. The lock nut is great to facilitate pumping your tires, but not needed once the tube is inflated. Like many other road cyclist I know, I don't even install it. I and I have never had an issue because of this. 

Generally you should look for tubes with a longer valve if you feel like the one you had was too short. AFAIK know they are available in three lengths. If you are experiencing recurring flats, you should investigate whether it always occurs in the same place and carefully examinate rim(and rim-tape coverage), and the tire. 

It's not unusual for the source of the issue(for instance a shard of glass) to be inconspicuously stuck in the tire.