Yes, for the same reason that we tell people who have gotten a sunless tan to be careful in the sun. A sunless tan does not protect the skin very much from the harmful rays of the sun, so I would think it would still be quite possible to get a tan from a tanning bed. However, I am curious why you would want to do so. My supposition is that you got the sunless tan to prevent sun damage.
The ingredient in most of these products is dihydroacetone. DHA acts by binding to the dead cells of the stratum coreum (horny layer which sits on top of the living skin.). This produces a color change which acts for about a week. Then those cells fall off and your sunless tan gradually diminishes. We dermatologists actually encourage these tans since they do no harm and may slightly protect the skin. I did say slightly since they are not a true tan.
There are other products which are so-called tanning accelerators. Many of these contain the amino acid tyrosinase, an enzyme which helps form pigment. Unfortunately, these accelerators do not work all that well; certainly not as well as DHA.
Bronzers can also be used but these are really not much more than pigment containing cosmetics, blush on steroids.
Every once in a while a pill with canthaxanthin pops up. The FDA strongly discourages ingestion of this chemical. While it does occur in nature, in fact Pacific salmon gets some of its pink color from it, and it is added to foods, the amount ingested is small. When consumed for tanning purposes the amount of canthaxanthin may be considerable and cause a problem with your retina and liver toxicity.
As a dermatologist, I applaud your use of DHA, but I just have to question your using a tanning bed. In this case, fake or faux as my Gallic friends would say, is better.