It it impolite to "informally" join or draft a group of cyclists?
It can be considered "impolite" by roadies, but not because of the bike you were riding or the fact you didn't take a pull (although I am sure some will argue for this).  The main reason random drop-in riders are generally frowned upon are because of:


the dangers associated with unpredictability of a new rider
lack of insurance coverage


Potential Unpredictability

New riders can behave unpredictable especially in a pace line.  In the same way, groups can  behave differently than you might expect even if you are an experienced road rider.  Jumping into a group without knowing what they are doing can lead to unanticipated behaviours which may or may not result in a crash.

From the groups perspective, they don't know if you are a stable rider or if you will try to ride too close and clip a tire.  They don't know if you will block one of them when they try to rotate their positions.  You are a complete unknown who has just shown up.  Most people are suspicious of unknown factors.  

Likely they have also spent a lot of time training.  Maybe they are racers.  Maybe they are getting ready for a charity ride.  It doesn't really matter.  The last thing they want is to get taken out by someone looking for a quick draft or thrill.

Anecdotal Experience - Collision

I was starting to get ready for for cyclo-cross a few years back in August and part of my route was on the road with a transition to some local trails.  On the transition from road to dirt I usually hopped off the road to the shoulder, scrubbed about 10 km/hr in order to make a sharp turn on to the trails.

On the road I was in my drops plugging away on an interval when unbeknownst to me someone on a road bike had snuck up behind and was drafting me (my road section began at the bottom of a hill so I suspect this played a big role with suddenly picking up a rider). I was pushing hard on the flat so I suspect he was drafting tightly. When I sat up, to get ready to transition onto the shoulder, he collided into by back wheel.  I hadn't hit the brakes yet, but he must have been drafting me tight enough that simply letting off the throttle was enough to cause a collision.  

Luckily we were both ok. I was livid that he was drafting me without notice and bent my wheel.  He was livid that I didn't continue my pull to where he figured I should finish (at the very end of the road).

This belies the danger of an uninvited riders. NO COMMUNICATION had occurred between either of us as a result there was an unanticipated maneuver which lead to an accident.  NO COMMUNICATION while riding in close proximity is dangerous.

Insurance

For a number of years I was on the board of directors and/or running a large cycling club in western Canada.  Insurance, believe it or not, is an important consideration for a club.  We can't hold training rides or other official club events without it.  One of the Caveats is that everyone on the ride must be properly insured. For a new rider this can mean signing a one-time insurance form.  For other riders it can mean belonging to either our club or another club and being a member of the local cycling licensing organization.  If an incident happens and someone is injured (I have attended many  ambulance visits over the years from group ride mishaps) and it is caused by a rider that showed up uninvited this could void the insurance coverage.  We would have to prove that you were not invited, and that we didn't mess up our insurance forms with respect to your unofficial attendance.  If people are recovering from injuries the last thing we all want is to deal with lawyers and a court-of-law.

We are not deliberately unfriendly

All the above reasons may seem very unfriendly, this is not the intended effect, it is just the consequence of the world we live in.  If you are interested in attending a club ride, contact one of your local clubs (a quick internet search away).  You will likely find that:


Most clubs will have a relaxed "C" group where you will be taught
the ropes.  
They will be able to go over group etiquette and how the group works. For example:


where we double up pace line;
where we single up pace line;
average speed;
how the group should operate around traffic signage; 
how to point out obstacles and road hazards to drafting riders; and
riding route

Most will not care what bike that you ride.
And finally, they can ensure you have filled out the proper insurance forms.