Yes, if your income is right at the beginning of a tax bracket, deducting from the taxable income (which is what Traditional 401(k) and Traditional IRA do) may drop your income so it is in a lower tax bracket. Roth 401(k) and Roth IRA are post-tax, and they do not affect the taxable income at all, so that obviously doesn't apply to them.
But I really want to point out that "dropping your taxable income to a lower bracket" is not useful in and of itself. What I am trying to say is that, given that you will reduce your taxable income by a given amount, I don't see any benefit of it causing your income to go to a lower bracket, vs. dropping the same amount but staying in the same bracket.
In fact, one could argue that it may be even "worse" for it to drop to a lower bracket, because that means part of your 401(k)/IRA is deducting income that is taxed less, so it is saving less tax; whereas if you had deducted the same amount, but your income stayed in a higher tax bracket, then your entire 401(k)/IRA is deducting higher-taxed income.
(Note: I am not saying that it is not useful to use 401(k)/IRA to lower your taxable income below certain levels. For example, eligibility for many tax credits, deductions, exemption from AMT, and other tax benefits often have an income limit, and using a 401(k)/IRA to reduce your taxable income in order to get under these limits is a common and useful strategy. However, these income limits do not correspond to tax brackets. And since the question asked specifically about going to a lower tax bracket, I am just saying that only going to a lower tax bracket, specifically, is not useful.)