Yes, you should be able to.
Technically, whether you had the SSN last year or not, you should not have filed Single. You should have filed either Married Filing Jointly or Married Filing Separately. To file jointly, you would have applied for an Individual Taxpayer Identification Number ITIN for her. If filed separately, you would not need to apply.
Usually, with the new SSN, the IRS does not allow you to go back and amend to claim certain tax benefits, for example, Earned Income Credit or the Child Tax Credit. For example, some people file with their ITIN which does not qualify them for certain tax breaks. After they apply for their new SSN, they go back to amend to reclaim those benefit which required the SSN. The IRS does not allow.
In your situation, on your amendment filing as married, if your spouse qualifies for any tax benefits which require an SSN, IRS would likely deny them.
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