I'll bet they do. The more the merrier. There's safety (for Hizbollah) in numbers migrating across the country.
Lebanon is a failed democracy. They want to nightlife and business activity without the security. Hizbollah is the government. Syria, while not a democracy is more of the same - titular leadership backed by the real muscle. The real muscle tries to avoid accountability at all costs.
The Danish Foreign Ministry has said that it expects to evacuate 1,700 people with a Danish passport or residence permit, through Syria. The Foreign Ministry estimated that 1,000 Danes could be trapped in southern Lebanon.