Uncomposted wood mulch used as mulch doesn't typically cause nitrogen deficiency except maybe to a small extent at the soil-mulch interface. That's why very small seedlings with shallow roots may have some problem whereas larger established plants would not because their roots are below the zone of decomposition. On the other hand if you incorporate the wood product into the soil rather than using it as mulch then there is a risk of nitrogen deficiency but people get around this by fertilizing with nitrogen to compensate. It's only going to cause a deficiency if you don't provide enough nitrogen to make up for the temporary deficit.
