Hi Abby. Most members of this forum probably play either piano or chromatic button accordion. So, it might be better to ask this question on the forum at melodeon.net. However, by my understanding of Irish and Cajun diatonic instruments (I don't play either of them - so get some opinions from others who do!), I would say the answer is "yes", up to a point.
Each row of a diatonic accordion (aka melodeon) plays the scale of a single diatonic key. The Irish two-row box has rows tuned to keys that are a semi-tone (half-step) apart. B/C and C#/D are the most popular. By playing across the rows and using the appropriate push or pull on the bellows, you can play all 12 chromatic notes, and thus tunes in several keys (theoretically, in all 12 keys, but in practice, only the common Irish keys).
The traditional Cajun box is a single row box with only 10 buttons and only the notes of one diatonic scale. Keys of C and D are popular, but boxes in other keys also exist. So, by using only one row on your B/C Irish box, you can practice playing a Cajun box tuned to the key of either B or C. This should certainly get you past the beginner stage.
Then there is the matter of the bass buttons, which are usually spoons on a Cajun box. The Cajun instrument will have only two buttons/spoons that play only the tonic and dominant bass notes and chords. For the key of C, this would be the C and G bass notes, and the C and G major chords. So, on your B/C Irish box, you would want to use only the two bass buttons that play this combination. The Irish box will probably not have tonic and dominant bass buttons for the key of B, since this is not a common key for Irish music (and also probably not for Cajun music).
In summary, your B/C accordion should have everything you need to get started playing Cajun music in the key of C. Most other types of two or three row diatonic accordions would also work in this way, by playing only one of the rows.
If your primary interest is Irish music, then let me suggest that mastering Irish music on the B/C (or any) box, and playing it well and up to speed, will take you many years. Cajun music is probably easier to learn.
If you find yourself pursuing Cajun music seriously and want to sound authentic, then you may want an actual Cajun box. The difference is that the Cajun box will have four reeds per note (rather than 2 or 3), it may have a different musette tuning, and will be tuned to just temperament (rather than equal temperament as on almost any other accordion).
If you decide to get a Cajun box, then a big decision is what key to specify. That might depend on the other musicians you want to play with. Fiddlers usually prefer to play in D, but I understand that some Cajun fiddlers tune down to C. I have observed that professional Cajun musicians usually have two or three boxes tuned to different keys.
I don't think I have ever heard Cajun music played on anything other than a single row diatonic. Zydeco, however, often uses other types of accordions, as well as the Cajun box.
