No. There is no guarantee of that.
Mortgage interest is an itemized deduction. You get no tax benefit from itemized deductions until all of them together add up to be more than your standard deduction.
2016 Standard Deduction
Taxpayer under 65, not claimed as a dependent
$6,300 for Single
$12,600 for Married Filing Jointly, or Qualifying Widow(er) with dependent child
$9,300 for Head of Household
$6,300 for Married Filing Separately
For over 65 or blind, add $1,250 for each instance or add
$1,550 each instance if single and not a surviving spouse.

Even so, you do not get the deducted amount back. Deductions reduce your tax by reducing your taxable income, the maximum benefit that you get is the amount of the deduction times your marginal tax rate.