A PC has a hereditary curse (originally inflicted on an ancestor) that means in a specific scenario the character dies instantly. The curse is coming from an evil god(dess) in Faerun.
Can anyone detect it easily just by casting Detect Magic?
You seem to want to run your deity strictly according to the rules. I want to say up-front that I think this is a mistake, because by definition deities shouldn’t be subject to the rules, and the rules available for them, from Deities & Demigods, are quite poor. But if you insist...
Detect magic would typically indicate that there is “some magic” on the subject, and with an appropriate Spellcraft check, what school of magic that came from (probably Necromancy, à la bestow curse) or even what precisely the effect is. However, since it was presumably the Lay Curse1 salient divine ability used to curse the target, and the Spellcraft DCs here would scale with half the caster’s level, that would presumably be a very difficult check indeed.
Note that skills do not automatically succeed on a natural-20, and this is a good reason why: it’d be preposterous for everyone capable of a cantrip or orison to have a 5% chance to succeed here. So if the DC is high enough, the only thing anyone will be able to detect is that there is some magic, with no details about it.
However, there is precedent for hiding magic from detect magic. Nystul’s magic aura can mask the aura of a magical object. If allowed to affect the victim (it is normally item-only), this would fool detect magic completely, and even identify would only function if the caster could make a Will save. Magic aura only lasts 1 day/level, but the Alter Reality salient divine ability can make it permanent (and also mimic magic aura in the first place, and since the magic aura came from a salient divine ability, it would not be subject to dispelling or suppressing, e.g. via antimagic field).
The spell read magic only allows you to read magical texts, scrolls and similar materials without actually triggering the spell (unless it's a cursed scroll).
Detecting a curse (and answering this question) requires more information regarding the curse itself, but generally it is very difficult to detect if a character is cursed in the way that you describe (I would not know of a method to do so).
Any caster of the 0-level Sor/Wiz spell detect magic [div] (PH 219), after 3 rounds studying an area, can make for each magical aura in the area a Spellcraft skill check (DC 15 + spell level). Success reveals the picked aura's school. Then for that aura the caster can make a Spellcraft skill check (DC 20 + spell level). Success identifies the spell in place, but the caster can make but one attempt. The DM may rule that such identification reveals the choices the caster made when casting the spell but, more likely, the DM'll only reveal the spell's name and description.
If the deity's spell is the typical 4th-level Sor/Wiz spell bestow curse [necro] (PH 203), this means a detect magic spell and a pair of Spellcraft skill checks (DC 19 then DC 24) reveals that spell as present on the creature but, probably, nothing else.
Thus the average, low-level wizard will probably learn that the effect's of the school of necromancy, and the average mid-level wizard will get both school and spell, but the thorp's local level 1 adept will probably just shrug his shoulders and say, "Yes, he is indeed magickified."
Note that a caster that uses the spell detect magic for 2 rounds learns the strength of the most potent aura in an area and at 3 rounds the strengths of all auras in an area. In most cases, this isn't particularly helpful, informing the caster only, for example, that of an aura's general category (like the moderate aura of the 4th-level spell bestow curse). However, a bestow curse effect generated by the salient divine ability lay curse will probably instead have an aura of overwhelming, being, by definition, deity-level in origin. Such an aura strength is a pretty clear sign that more impressive forces are at work, and this knowledge can be gained by even a lowly apprentice.
It sounds like this curse might be more complicated than the run-of-the-mill curse casters bestow. If so, the 3rd-level shaman spell detect curse [div] (Oriental Adventures 100-1) might be in order. The spell instantaneously reveals if a creature, object, or area is cursed and a successful Spellcraft skill check (DC 20) reveals the curse's general nature (and what general nature means is up to the DM but I'd expect more than what would be revealed with a simple detect magic from a 3rd-level spell). Since pretty much nobody plays a shaman (Oriental Adventures 22-4), a creature will likely have to employ the skill Use Magic Device to cast the spell from a scroll (if one's even available).
While it sounds like this series of events might be simply narrative license, it's possible for anyone (even a sufficiently powerful PC) to hex a creature's bloodline by employing the criminally underused and plot-generating 8th-level Sor/Wiz spell familial geas [ench] (Heroes of Horror 129). The target is affected by a geas and when the target dies the spell's effect affects the target's nearest living adult relative, and, once established, the effect can be removed only by a remove curse spell from a caster 2 levels higher than the original enchanter, a miracle, or a wish. It's a fantastic spell for DMs.