Although it would be great if plan documents and/or written procedures dealt with this up front (and many do), I don't think it would be a plan failure to withhold taxes and amounts that had been elected, e.g. health plan contributions, before 401(k). The 401(k) plan is just one claimant among several others with lawful claims on the paycheck, e.g. Uncle Sam for FITW and FICA, state tax withholding, short-term disability, health plan, cafeteria plan. They all have legal claims on the money and the precedence among them should be based on the employer's reasonable triage of these claims, which would probably put the 401(k) plan last. You will probably want to amend the document pronto, however, if it can be read not to allow such flexibility, but I have never seen a plan document that would put deferrals ahead of taxes or other lawful claims. At worst, the wording is simply oblivious to this foreseeable practical issue.
To paraphrase someone's statement regarding the Constitution (think if was Marshall), "It's a 401(k) plan, not a suicide pact."