Can we use participle clauses as adverbial modifiers?

Most of the time, participle clauses are used in sentences like the ones that I have written below (all of which feature present participles):

[1] Walking the dog, she breathed the fresh air.

[2] He saw the woman walking the dog.

[3] He saw the walking woman.

However, on occasion, I will encounter sentences such as example [4], a partial quote from author Robert Ludlum's The Bourne Identity.

[4] She opened the door and for a moment he stood looking at her ….

This breaks the standard format that most participle clauses take, featuring no comma and modifying the verb 'stood'. That said, can a participle clause function adverbially in this way? If so, does the same apply to past participle clauses?

Participle clauses used as adverbs of manner are a particular category. they do have adverbial meaning and function, but they do not always meet all the aspects of the normal behaviour of an ordinary adverb of manner. An interesting article, The Use of Participles and Gerunds expresses my view on the matter. On p. 44 the author writes:

Present participles used to express manner/accompaniment (or attending circumstances). A participial phrase showing accompaniment cannot well be converted into an adverbial clause. But beyond doubt, it has an adverbial function, and can be regarded as an adverb of manner, or of attending circumstances, so to speak. We usually use a participle to indicate manner after such verbs as arrive, come, go, leave, lie, run, sit, and stand, etc. For example:

• The whole family stood waving in the road. (accompaniment)

English resources names this use more simply:

The present participle after verbs of movement & position *She came running towards me.

Yet it does look like your sentence fits this description as well:

When two actions occur at the same time, and are done by the same person or thing, we can use a present participle to describe one of them. When one action follows very quickly after another done by the same person or thing, we can express the first action with a present participle.

• They went laughing out into the snow. = They laughed as they went out into the snow.

So your sentence

he stood looking at her …

does show simultaneity of action and manner: He was looking at her as he stood/he stood while looking at her/ he did not simply stand, he stood looking...

It is however clear to me that whatever category you put it in, it remains an adverbial.