[RPG] Does a Tower Shield providing Total Cover in a 5-foot doorway block Channel Energy from going through

Necromancy is not inherently evil

Necromancy spells are only characterized by their use of negative energy; negative energy is entropic in nature but is not a moral force. The inflict line of spells, for example, aren't evil.

But...

Necromancy does have some evil spells. Thankfully, they'll helpfully be labeled [Evil] in the spell descriptions!

Spells associated with particular alignments are indicated by the chaotic, evil, good, and lawful descriptors in their spell descriptions.

Per the Cleric class description, the Cleric cannot use spells with an alignment component opposed to their own; Good Clerics can't use [Evil] spells, Evil Clerics can't use [Good] ones. When in doubt, just check the spell's description!

Further, Channel Energy does not affect non-spontaneous spellcasting. While Channel Energy determines what spells a Cleric may cast without preparing, it doesn't affect spells that the Cleric memorizes ahead of time and does not otherwise restrict their casting list, though their alignment may do so (see above).

Funnily enough, works by RAW.

There is no prohibition of magical healing in construct traits, though some constructs are explicitly immune to magic except select few effects.

There is also no prohibition in the heal spell.

Technically, you can do it, but expect a heavy book thrown by your DM. He will also probably houserule it away, at least I personally would.

Note:

Can't remember anything on that in 3.5 either, though the description of Warforged contrasts the possibility of both special and positive-energy healing (emphasis mine):

As living constructs, warforged can be affected by spells that target living creatures as well as by those that target constructs. Damage dealt to a warforged can be healed by a cure light wounds spell or a repair light damage spell, for example, and a warforged is vulnerable to disable construct and harm. However, spells from the healing subschool and supernatural abilities that cure hit point damage or ability damage provide only half their normal effect to a warforged.

That leads one to the implication of impossibility of positive-energy based healing for a regular construct, even if it is not stated anywhere.