Is Teeth Whitening Possible for People with Receding Gums?

With proper pretreatment it is possible . The area of recession has very little or no enamel and well only marginally whiten. I usually suggest changing your brush to a SoniCare (non abrasive whitening Toothpaste) and using your opposite hand to brush so you can not scrub eroding more enamel. I then make bleaching trays and have the patient use MI paste in the trays twice per day to remineralize and desensitive your teeth. After several months of this usually a patient can bleach with no problem.

At bleaching process your dentist is protecting your gum and naked root area to avoid the pain and post-up sensitivity. Generally , all whitening procedures have pain or sensitivity for short time. Also application of fluoride after whitening is helping you to avoid the sensitivity.

The sensitivity caused by whitening procedures is typically temporary and only lasts about a day or two if sensitivity is experienced at all. 
For patients with recession the doctor can protect the root surface while the treatment is being performed.

Ideally the tooth whitener should not contact the root structure that is exposed from recession.
With any of the at-home treatments it is very hard to keep the peroxide localized to the enamel. The paint on treatments immediately wash off the teeth; the strips are not customizable.
The best way to address this issue is to have the dentist apply the whitener in-office such as the Zoom treatment, which can avoid the recssion areas. Another suggestion is to have a tray made by your dentist, cut short of the recession.

It is entirely appropriate to whiten your teeth with receded gums. Use a strong Fluoride toothpaste (Fluoridex) prior to and during the treatment for a minimum of 1 week. Keep in mind any exposed root surface will not whiten, only the enamel. 

While you may experience an increase in sensitivity while whitening your teeth, it should be temporary. Essentially the process dries out your teeth, so when you are done and the teeth re-hydrate, the teeth should be fine again. In your case, still sensitive, but not as bad as during the procedure.
But DURING the process, there are things that can be done to minimize the pain. Trays can be fabricated short of the gum line, but the tray material needs to be fairly rigid (otherwise the gel will leech out to the receded area). In office procedures can block out the recession, so that option should be considered as well.
You should consult your dentist on WHY the gums have receded and consider fixing the problem before whitening.