No, the limits are separate.
If you and/or your employer contribute to the Simple IRA at any point during the year that does mean you are "covered by a retirement plan at work" which effects deductibility of traditional IRAs for both you and your spouse, but it doesn't effect Roth IRA eligibility.
Anything in a Simple IRA will also be a previously deducted IRA balance, so it would cause issues if you wanted to make a backdoor Roth contribution (non-deductible traditional IRA converted to Roth IRA) as the conversion would be taxable in proportion to previously deducted to non-deductible balances.
