Redundant? Almost completely.
These words overlap 90%, and the tiny 10% difference isn't really enough to avoid being redundant, even if a shred of difference is truly present. Redundancy is measured in degree of overlap versus the degree of separation.
Second problem: these words tug their connotations in opposite directions, which muddles the already tortured meaning.
Conclusion: zero style points for using these together. Their incomplete overlap is a technicality. They are redundant enough.
BTW: this is a great family of synonyms relating to bevity of language:
*) Terse is tense and possibly rude. Brief, yes, but not in a good way.
*) Succinct speaks lucidly. Brief, yet clear.
*) Concise contains a lot despite its small size. Brief, yet comprehensive.
*) Laconic is just brief; it doesn't hint at other virtues. Unlike terseness, its connotation is usually neutral, and it alone is useful among this synonym family for describing an individual's personality generally (versus their specific words).