It depends (but likely no).
IMO, duct cleaning does have it's place in today's world (pet hair/allergen reduction for example). However, it likely only needs done once every 10-15 years in most cases.
Duct sealer is basically like the sealant you can put in a bicycle tube to fix a leak except that since ducts aren't a completely closed system like a tube, it will either dry (sealing) or be evacuated when the process is complete. Its also airborne instead of a sludge/goop since it needs to travel large distances. It will travel through the ducts and seal any small gaps in corners of ducts or along the seams. The intent is to reduce air loss into what would be presumably the structure of your house (inside walls and ceilings) by making sure everything that goes in (at the furnace/ac blower) comes out an open vent.
The following is what my HVAC installer (not the sales man) told me when they installed my new heat pump. Unless your home was designed to be air-tight (with the appropriate filtration/recirculation systems in place to bring in fresh air), there is little to no gain to be had by sealing your ducts. If you were going to retrofit an existing non-airtight home to be airtight, my guess is that the duct work would need to be mostly replaced anyway (especially returns since they frequently run between joists with no actual ductwork in places) and even if you didn't replace the ductwork, sealing the existing ducts would be near the bottom of the to-do list. Lastly, They probably didn't tell you this but depending on the ductwork in place, it may take more than one application to actually seal the holes since the sealer, will seal only very small gaps and you will have to build up layers. No idea if the price you were quoted assumed a single application or if they quote for a "complete job".
Since I declined the service, I didn't ask about the contents of the sealer itself but there is mention of this (that it is pretty much an unknown) in the EPA document below.
Here is a link to the EPA document that another answer mentioned:
The first sentence is:
Knowledge about air duct cleaning is in its early stages, so a blanket recommendation cannot be offered as to whether you should have your air ducts in your home cleaned.
There are two sections of that document that apply directly to your question:
Should chemical biocides be applied to the inside of air ducts?
Do sealants prevent the release of dust and dirt particles into the air?
Manufacturers of products marketed to coat and encapsulate duct surfaces claim that these sealants prevent dust and dirt particles inside air ducts from being released into the air. As with biocides, a sealant is often applied by spraying it into the operating duct system. Laboratory tests indicate that materials introduced in this manner tend not to completely coat the duct surface. Application of sealants may also affect the acoustical (noise) and fire retarding characteristics of fiber glass lined or constructed ducts and may invalidate the manufacturer's warranty.
Questions about the safety, effectiveness and overall desirability of sealants remain. For example, little is known about the potential toxicity of these products under typical use conditions or in the event they catch fire.
In addition, sealants have yet to be evaluated for their resistance to deterioration over time which could add particles to the duct air.