It depends on whether or not your employer did the "deductible funding" portion correctly through an HRA (Health Reimbursement Arrangement), and whether or not they have professional administration of that benefit. If they have an HRA, with a plan document, and that HRA is professionally managed, then the payment should go through without a hitch. If there is no HRA plan document and your employer is just doing this informally, that's another issue.
What IndividualHealthGuy was trying to explain in his prior post, is that you can continue HRA benefits under COBRA. Following is a link to an IRS document that explains that you can keep the HRA benefits under COBRA - http://www.irs.gov/pub/irs-drop/n-02-45.pdf. To make it easier, let me quote part of it that answers this question for you:
What IndividualHealthGuy was trying to explain in his prior post, is that you can continue HRA benefits under COBRA. Following is a link to an IRS document that explains that you can keep the HRA benefits under COBRA - http://www.irs.gov/pub/irs-drop/n-02-45.pdf. To make it easier, let me quote part of it that answers this question for you:
An HRA is a group health plan generally subject to the COBRA continuation coverage requirements. If an individual elects COBRA continuation coverage, an HRA complies with these COBRA requirements by providing for the continuation of the maximum reimbursement amount for an individual at the time of the COBRA qualifying event and by increasing that maximum amount at the same time and by the same increment that it is increased for similarly situated non-COBRA beneficiaries (and by decreasing it for claims reimbursed).