As long as it tastes acceptable, yes, you can eat the asparagus.

The reason that it decays from the tip down is mainly the nature of the tissue; not many people who have never worked with asparagus realise that those stubby "spears" are the buds of the long, wiry, often thorny, fronds of the asparagus plant. We have may wild species of Asparagus in Southern Africa, and some of them are appallingly thorny; they have vernacular names that translate as "cat thorn", "wait a little" and the like. However, each barbed-wire frond grows from the expanding soft tissues of the underground spears. Apart from the berries and certain underground storage organs of some species, both of which are excellent in salads, the spears are the only edible part; the spears of even some of the most vicious species are delicious, some, though smaller,  being tastier than domestic varieties. The entire frond grows out in a matter of days. Now, fibrous, woody tissue cannot do such things, so the plant essentially builds an inconspicuous underground store of soft, crisp tissue, then when all is ready, it shoots out, thinning, branching and hardening as it goes.

We of course, don't want woody salads, so we harvest the spears just before they launch themselves at the great outdoors. Their stems are already starting to become fibrous, but the tips are the tenderest bud tissue. Anything that damages its easily bruised cells makes them available to microbial decay, so the tips decay fastest. Also, the tips are where the stored sap is being delivered to at the greatest pressure, so damaged or weakening cells at the tip tend to let the sap escape most and soonest. In some varieties at some stages, it is possible that some of the fluid you mention could be guttation, in which components of sap exude from special pores in stem or leaf buds, but it amounts to muc the same thing from your point of view.

In either case, it is quite safe to eat while it is reasonably fresh, and usually afterwards too.