In English, can a whole syllable be aspirated?
Solution 1:
There is no such thing as, "The whole syllable is aspirated." What you are describing is breathy voicing of the vowel, probably. 'Tis not aspiration.
Non-nasal stops may be aspirated. In some languages, voiceless (non-nasal) stops can be preaspirated, but typically aspiration occurs upon the release of the stop. Both voiced and voiceless stops can be aspirated, as shown in many languages of the Indian subcontinent.