Learn Danish: Manden er i gang med at pakke udstyret, så teltet er klar. - The man is packing the equipment so the tent is ready.

Yes, you can. In Danish, så and så at can both be used to mean 'so that' to show the purpose or result of an action. Dropping the at and just using så is much more common in everyday speech, while så at sounds a bit more formal.

Does så introduce a main clause or a subordinate clause here?

When så means 'so that' (indicating purpose or result), it introduces a subordinate clause. This is important for word order if you add an adverb like ikke (not). In a subordinate clause, the adverb goes before the verb: ... så teltet ikke er klar.

Why use er i gang med at pakke instead of just translating 'is packing' as a single verb?

Danish does not have a direct equivalent to the English '-ing' tense (present continuous). To strongly emphasize that an action is happening right at this exact moment, you use phrases like er i gang med at (literally 'is in going with to'). You could simply say Manden pakker, but it loses that active, ongoing feeling.

teltet is a neuter noun (an et word). Why doesn't the adjective klar get a -t at the end?

klar is a slightly tricky adjective. When it means 'ready', it usually does not take the -t ending, even when describing neuter words. If you were to say teltet er klart, a Dane would likely understand it to mean the tent is 'clear' (as in transparent or obvious) rather than 'ready'.