For a C(13) chord do you add the 7 and 9 as tensions by default (C, E, G, B, D, A), or would the chord then be a C(7,9,13) chord, and the C(13) chord be (C, E, G, A)?

Definitely the former. I tend to like jazz theory over traditional classical theory (as it generally makes more sense) and jazz theory would call the latter a C6 chord, while classical theory would probably call it an Amin7 inversion. A C13 chord should really have the 7 and 9, and possibly even the 11, though it's usually more acceptable to omit that.

thanks!

Actually it depends on what you are really asking.

"C13" is a dominant seventh chord. Therefore it can include the minor 7th and the major 9th such as C,E,G,Bb,D,A.

"CMaj13" is a major seventh chord. It can include the major 7th and the major 9th such as C,E,G,B,D,A.

A "C(13)" chord would usually be interpreted as a C triad with ONLY the 13th added. Note the use of parentheses to convey the different meaning of C,E,G,A.

If you want to be geeky about things...
The "C(13)" is essentially the same structure as a "C6" as Noah explained. Some musicians, particularly arrangers, may make a subtle distinction bewtween the 6th and the 13th in the way the chord is voiced and how voice-leading is handled. For example, a "C6" may be used for tonic harmony (i.e. a "I" chord in key of C) versus a "C(13)" for dominant harmony (i.e. a "V" chord in key of F). However this is getting to the point of splitting hairs, and one can definitely find exceptions to this example.

Finally, there is much confusion and disagreement as to the role of parentheses and labelling in chord symbols. I have seen "C(13)" written when people really want "C13" and different publishers and arrangers have different conventions. Take that and the harmonic context of the written chord into consideration if something doesn't sound right.

Generally (and I've played Jazz saxophone for many years), the flat-7, 9, 11, and 13 are all fair game on any chord specified as a X7, X9, X11, X13, or X6 chord. They're all dominant chords. However, if something other than the 7 is specified, there's generally a reason (like a strong melody note), and it should probably be highlighted in some way.

Tom