I'm married w 1 child but have to claim single/0 on my W4 to get enough withheld. If I changed married/1 and put the extra cash in a 401K, would my tax bill go up?

I am married with a dependent but claim single/zero on my W4 in order to have enough withheld.  My wife claims married/1.

What would be the impact to my Federal taxes if I switch to married/1 on myW4 and contributed the additional take-home pay to my 401K,?