Can I contribute to an ira or roth to the maximum and not deduct it ?

For traditional IRAs, yes.  Anyone with earned income can contribute, but there are limitations for deducting it. 

Roth IRAs are never deductible but you cannot contribute if your income is greater than:

$194,000 if Married Filing Jointly;

$132,000 for Single or Head of Household;

$10,000 if Married Filing Separately.

"If the income is greater than $194,000" Is that gross income or Adjusted Gross Income?

AGI

Does a contractor's 1099 income count as "earned income"?