(1) "The spectators leaped to their feet, roaring approval."
Modifiers modify not sentences or clauses, but words.
Present participles like "roaring" are usually adjectives and as such usually modify nouns or pronouns.
Adjectives should modify the first noun that precedes them or more rarely the first noun that follows them.
In the sentence you have it is the spectators who roar, not their feet.
Therefore the sentence should read "Roaring their approval, the spectators leaped to their feet" or "The spectators, roaring their approval, leaped to their feet". I prefer the first possibility, because it does not separate the spectators from what they do, which is roar.
(2) "The spectators leaped to their feet, and they roared approval."
Verbal phrases such as "leaped to their feet" modify nothing. When introduced by a coordinating conjunction they simply form compound sentences, as in your example.
A subordinate clause introduced by a relative pronoun or a subordinating conjunction can act as a modifier.
However, since the roaring approval is really the focus of the sentence, it should be the leaping to their feet that is subordinated.
As they leapt to their feet, the spectators roared in approval.
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