Traditional IRA contributions can be deductible or nondeductible depending on MAGI for determining deductibility (the MAGI referred to in the answer above) of the contribution. However, since you are asking about Medicaid MAGI, it seems that your MAGI for determining the deductibility of a traditional IRA contribution would certainly be low enough to allow a full deduction for a traditional IRA contribution. Of course, to be able to make any traditional IRA contribution you must have sufficient eligible compensation to support the contribution.
Yes, elective deferrals to a 401(k) would reduce your W-2 taxable income (or would provide you with a self-employed retirement deduction) that would reduce your AGI and therefore reduce your both your Medicaid MAGI and your traditional IRA deductibility MAGI.
