Short answer: No. To use ICHRA funds you must be enrolled in qualifying individual coverage or Medicare. Coverage under a spouse’s group plan doesn’t qualify, so you couldn’t be reimbursed through the ICHRA while on that plan.
An ICHRA only reimburses employees (and dependents) who have qualifying individual-market coverage or Medicare; that’s a condition of the tax-free treatment. Being enrolled in a spouse’s employer group plan is not individual coverage, so it doesn’t satisfy the ICHRA requirement, and you couldn’t draw the allowance while relying on the spouse’s plan. Your choices would be to enroll in your own individual plan to use the ICHRA, or decline the ICHRA and stay on your spouse’s coverage. Note an ICHRA offer (even if you decline) can affect your eligibility for a premium tax credit.