I don't think that Bradstreet necessarily implies that man will "glide along happily" in life (catastrophe or not). In Stanza 29 of her poem she mentions that man might never find cessation from "sorrows, losses, sickness, and pain" (199).
Similarly, Bradstreet's version of happiness (or going through life happily) is closer to contentment than it is to what we might think of happiness today. While she does mention a mariner sailing through life with ease and then encountering a storm and wishing for calmer waters (Stanza 31), the next stanza (32) addresses Bradstreet's true perspective. She writes that after man is done partaking of the pleasures of this world,
"sad affliction comes and makes him see / Here's neither honor, wealth, or safety. / Only above is found all with security" (222-224).
It seems that the poetess's actual message is that when one seeks contentment and happiness elsewhere, it usually takes a catastrophe to show him the source of true happiness and "security"--God. This is in keeping with Bradstreet's religious perspective.