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I have data that is accurately positioned with the NAD 83 MTQ Lambert EPSG:3798 projection.

If I reproject this data in EPSG:3857 (web mercator) the markers are no longer positioned accurately on the tile layer. Is it possible to use CartoDB, or Leaflet, to use a different projection than EPSG:3857?

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Try projecting your data to 4326 (WGS84) instead of 3857. Leaflet expects coordinates in geojson to be 4326.

It'll probably easier to reproject your data before including it your app rather than adding Proj4Leaflet to do on the fly reprojection. Plus, if you don't use Proj4Leaflet, that's one less dependency in what you're developing.

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