I vote "Yes", but with a few qualifications. At the risk of sounding a bit preachy...
With the widespread prevalence of cellphones and 911 systems populated with folks who are paid to take emergency reports for a living, an attempt to call in doesn't cost much. If the line is perpetually busy, then you can probably assume that they already know about the storm and are taking calls on it. Good operators will not be upset at you making a report if they already know about the storm. If they don't need any further information from you, they'll tell you tersely that they already know about it and will politely disconnect you and move on to the serious calls. Sometimes, though, they may want to get some critical information (size of storm, touchdown condition, direction of motion, nearby structures and towns, etc.) that spotters or the general public have not yet revealed to them. 911 operators are generally trained to collect such valuable information and will ask you for it if they need it.
I am surprised at the indications that any NWS local offices in tornado-prone areas do not have some sort of telephone hotline. We do, here, and they frequently ask for reports from the public (not just spotters, but the general population) right in the text of both severe thunderstorm and tornado warnings. Even if this information goes right into a tape recorder and you don't actually speak to the officer involved, the officer can listen in to the line and get valuable information, as it happens. They particularly appreciate public reports of confirmed funnels and touchdowns, since the population here is relatively skeptical about radar-indicated warnings.
My qualifications for the "Yes" vote apply to chasers who maintain CB and ham radios, or who use a scanner set to monitor the transmissions of emergency service agencies of the area. If by some means, you can determine that emergency personnel are already aware of the event and that their information is accurate, then making another call would be counterproductive. Of course, if the information you hear is incorrect, then you should still call in and report the discrepancy, in a non-confrontational way. Just tell them what you know and let them make the decisions. Also, if conditions change (i.e. another touchdown), then a call would be very useful, since the attention of both spotters and emergency services may be too focused on the first event to miss new developments.
Compare the situation to the traffic accident analogy mentioned before. If you see three people with cellphones at the site, see other drivers helping out, hear the sirens, or see the emergency vehicles on the way, then another call wouldn't do much good. On the other hand, if these things aren't happening and everyone just assumes that someone else has called or that the authorities will take care of it, help will never arrive.
Another qualificatin involves a bit of research. It doesn't hurt to sniff out the preferences of the authorities and the health of the spotter network in the place you plan to chase, if you're not familiar with the area. Most police, for example, won't mind a call to the non-emergency number to find out what they would prefer for you to do, if you have enough lead time before the severe weather begins. If you know that you're in an area with a superb spotter network or a place where officials would be bothered by redundant reports, then your call may not be necessary or welcome.
Common sense goes a long way, too.