Hi Jules,
From your description, "intro to scuba" (other names: "resort course", "discover scuba diving"), is something I have seen, and the safety of the activity depends on the dive operation and the instructor in question.
As a "warm water wimp", I travel to dive, have dived with operators in a variety of locations, and have had the chance to observe several of these "courses(?)" conducted, both the in-water and topside components. I once "sat in" from a distance- with the instructor's permission-as a nondiving friend took such a course.
The three components- "lecture", "pool session", "dive" seem pretty standard, but I have seen a wide variety of levels of

rofessionalism/ concern/ attentiveness etc.
The best, IMO, had detailed-but not to the point of "overkill" - "poolside" explanations of the equipment, techniques, and procedures to be learned, followed by an in-water "pool session" to reinforce these ideas and to let the "student" demonstrate the skills, followed by a shallow, closely monitored dive, where the "students" were accompanied by instructors/DMs-who had no other responsibiltites at that time than to supervise and assist the students.
The worst-again IMO- gave little time to the explanations, some time in the pool, and -the very worst- put the students into the actual dive with no more assistance/supervision than that given to the certified divers.
With all that, is what you are going to do safe? Probably, but be sure to ask any questions, get a feel for the level of attention given to you, and don't hesitate to speak up if you are uncomfortable with anything. [ That's a good rule for any dive situation-certified or not]
Regarding "should you be certified" as I said above, "resort courses" can be safe, and will be less expensive than a full certification course, perhaps a consideration if you are not sure you wish to become a diver. But if you REALLY want to dive -and the Caymans is a great place to do that, then getting certified "at home" would be the way to go. Falling somewhere in between could be: do the "classwork/poolwork at home (local LDS)and do the certification dives-and more- while on vacation. That, however, would need to be set up in advance.
Regarding Seasickness- it isn't the depth you are at -it is the movement of the boat /surface chop (and sometimes the current whileu/w) that creates that awful experience.
I'd suggest being prepared for that possibility. There are a variety of threads on that topic on this board,-I'd suggest doing a
"search" and get the full picture.
Whatever you decide, good luck, and enjoy.
MIke