Is it true that alcohol can cause high cholesterol?

No. Alcohol in low doses (1 drink per day) can raise the good cholesterol (hdl), and sometimes social drinkers will have high total cholesterol because their good cholesterol is high. If the bad cholesterol (ldl) is ok (under 120 is recommended), there is no problem. Alcohol can and does raise free fat levels in blood (triglycerides) and this is not healthy for the heart or the rest of us.
Unlikely. This is unlikely because alcohol tends to lower cholesterol levels when taken in moderation. Excessive use would "kill" the liver, the main site of cholesterol production, so if the liver is sick then there will be less cholesterol produced. It may, however, not hold true for people with genetic disorders of cholesterol metabolism, in whom cholesterol may remain elevated despite the above.