Then I would recommend that you consult with your doctor.
The two laws I referenced are the Family Medical Leave Act (FMLA) and the Americans with Disabilities Act (ADA). FMLA refers to time off work; the ADA refers to accommodations on the job. They are not mutually exclusive but at the same time, the criteria for eligibility are not the same. It is possible to be eligible for one but not the other; it is also possible to be eligible for both (or neither).
You meet the criteria for FMLA, which means that you could take up to 12 weeks of protected medical leave - IF your condition qualifies under the FMLA statute. Your doctor will know if it does or not. If it does, you cannot be fired or otherwise treated adversely BECAUSE you took the leave. However, FMLA does not protect you from a termination or an action that would have happened whether you took leave or not. I mention FMLA only in the interests of being thorough - I really don't think FMLA is going to do you much good unless that leave is going to allow you to return to work with your productivity issues solved. Discuss it with your doctor.
Outside of confirming that your employer is subject to the ADA (which it is, based on your answers above) it's not possible for a message board to determine how to apply the ADA. Under the ADA, if you have a qualifying disability (and we do not know if you do or not; the temporary one is not since temporary disabilities are not covered under the Act but the permanent one may or may not be - we can't say based on what we have) you are entitled to a REASONABLE accommodation that will allow you to perform the essential functions of your position to standard. Remember what I said above; there are NO circumstances under ANY law where an employer is required to accept sub-standard work.
You are not required to complete the form under the law. However, if you do not, you have no protection under the ADA. (You may not have any with the form, depending on circumstances a message board cannot assess, but you definitely have none if you don't.) If your productivity issues have reached the point where your employer is voluntarily offering to provide an accommodation, that's not a good sign for your continued employment without whatever protection you can get. Keep in mind that the onus of providing FMLA protections is on the employer, but it's up to you to ask for protection under the ADA. The employer is not required to assume such protection is needed. So they're already doing more for you than the law requires, just by offering you the opportunity to request an accommodation
What I'm getting from your post is that your work product is sufficiently poor that your employer is having to consider taking action, but you are well enough thought of that they don't want to fire you outright. It's not your evaluation of your work that matters, it's theirs. So take that form to your doctor, Ask him if he thinks either law is applicable, and what accommodations would be reasonable. Then complete the form and take it back to your employer. It's not by any means a guarantee, but frankly, completing that form is the best option you've got.