Yes. Strengthened by a master of the Ring, a Gondorian army would have been harder to defeat than if only led by someone like Denethor.

: And yet some of the estimates seem too low for a "formidable"
: power.

Well, it's relative to what we know of Middle-earth. The time period is roughly 4,000 BCE, and though the implied population of the world is quite small compared to the estimates anthropologists suggest for that time, the armies are immense compared to what history and archaeology suggest. Tolkien's knowledge of the past would have been less than our own today, because we have benefitted from several additional decades of research and analysis.

So, you have to keep in mind that the story is set in an imaginary time at the end of a "forgotten golden age" where things were bigger and better than we now recall. And yet that time was a transition between the "golden age" and real history.

It would be several thousand years before large armies evolved "again".

: And what strategy did Gondor have? Merely defensive?

In Denethor's time Gondor's strategy appears to have been twofold: fortify the towns and coasts against invasion and harass the enemy's overland supply line through Ithilien.

: And how long had they (or Denethor) suspected that Mordor would
: mass an assault? Spying surley must have gone both ways, though
: it appears the only intelligence gathered was by way palantir.

Well, Sauron did not declare himself openly until 2951. Prior to that time it would have been unreasonable to expect an overwhelming war from Mordor, but attacks by Orcs (even large ones) had occurred. So Gondor was already in a constant state of war on its eastern border.

After Sauron declared himself Ecthelion appears to have been influenced by Aragorn to undertake some pre-emptive actions. They knew war was inevitable, but Aragorn fought a delaying strategy, so he attacked and burned the fleet at Umbar (the only specific example Tolkien gives, but his story implies there were other battles).

The burning of the fleet may have occurred in 2980 or 2979. If so, this would put the event only about 40 years before the War of the Ring. The Corsairs would have been able to rebuild their fleet in that timespan, but (being no expert on ship-building) I'm not sure of how long it would take them to construct fifty great ships any many (perhaps hundreds) of smaller vessels. And it may be some of the ships taken at Pelargir were Gondorian vessels, since the harbors were still useful and Aragorn himself had sailed to Umbar.

Sauron's first major attack, however, occurred in 3018. That was when the Lord of the Nazgul took Osgiliath. Boromir says that only a remnant of Gondor's eastern force came back from the assault. This implies that Denethor lost the greater part of an army, several thousand men.

: Did his sense of hopelessness keep Denethor from acting to beef
: up the professional army? It seems to me, and I'm no tactician,
: that if I had a known foe bordering me, I'd be relying on a
: more professional army rather than irregulars or amateurs. And
: even the amateurs should have received annual (or more)
: professional training.

I think Martin and I agree on one point: regardless of whether the Gondorian was composed of mostly professionals or mostly militia, Denethor did what he could to strengthen it. His limitations would be economics (men must be paid, housed, equipped, and fed), training/drilling time, and available manpower (even in a pre-industrial society not every man would be acceptable for service in the army).

: Boromir was an exceptional warrior, but if a Gondorian soldier
: could do even half or a quarter of the damage that Boromir did
: in his final battle, Sauron would have to field an army five to
: ten times as great to insure victory wouldn't he? And who were
: the majority of soldiers in Saurons army? Orcs? A good
: profesional army, well led, even though outnumbered, should
: have been able to defeat a very large number of orcs, who
: seemed to be canon fodder whose only tactical purpose was to
: wear down the opposition.

Although the Orcs do come across as cannon fodder, they actually were very deadly and efficient soldiers. It was Orcs (primarily) who wiped out most of the Noldorin forces of the First Age.

Boromir implies at the Council of Elrond that Mordor's superior numbers alone would not have resulted in the loss of his army -- the Dunedain were still superior soldiers. It was the power of the Lord of the Nazgul that brought about the defeat, more than anything else.

: At any rate, some of the estimates of army size seem too small
: for a kingdom that otherwise sounds so grand.

We cannot really know sort of overall numbers Tolkien had in mind, but Gondor in the War of the Ring was only a shadow of its former self.

I suspect that Aragorn was probably leading 30-40,000 men abroad in future wars, but that would also include Rohirrim.

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