Yes, but it's a long trek - allow 2+ hours travel time each way. From Blowing Point on AXA you take the ferry to Marigot on SXM. You can than take the ferry from Marigot for the 1.5 hour trip to Gustavia. Be warned the ride over can be "lumpy" (many describe this ferry as the vomit comet). As an alternate you can take the "Fast Ferry" from the Chesterfield Marina (cut's the ride down to about 45 minutes).
You might want to consider flying from SXM to SBH. Check WinAir for schedules and rates (www.fly-winair.com
) to see if timing works for you.