Does adding a deck change the odds?
Adding an extra deck definitely increases the chance that someone will get a Canasta because cards are drawn without replacement.

The point is easiest to see via a drastic oversimplification.  Take a number of decks, take out six cards that are the same from those decks, shuffle the remaining cards together, and then try to draw a seventh card to match the six.  Each deck you add contributes 54 cards in general (because of Jokers), 10 of which match (because 2s and Jokers are wild), but you have to subtract 6 from both the card total and number of matching cards for the six cards you have taken out to start.  The probability that the next card you draw matches the six you have of that with various deck sizes is as follows:

1 Deck: (10 - 6) / (54 - 6) = 8%

2 Decks: (10*2 - 6) / (54*2 - 6) = 14%

3 Decks: (10*3 - 6) / (54*3 - 6) = 15%

4 Decks: (10*4 - 6) / (54*4 - 6) = 16%

5 Decks: (10*5 - 6) / (54*5 - 6) = 17%