Yes, most low-cost digital meters have a couple of current (ammeter) ranges, but they don't measure very high amounts of current. That's OK, though, because your drain is probably a pretty low-current one.

Don't confuse voltage and current. Current is proportional to the number of electrons flowing in the circuit, while voltage is proportional to the amount of "push" that each electron has. You always have to measure current in series with the circuit (e.g., as discussed above, by disconnecting the positive battery cable and hooking the ammeter up in a series with the battery post and cable.)

If you wanted to measure or monitor the charging voltage at the battery, you would of course leave both battery cables connected and simply connect a voltmeter across (i.e., "in parallel with") the battery terminals. (But what purpose would this serve, since your dashboard gauge does the same thing, doesn't it? If you had a problem with your charging voltage, wouldn't your dashboard gauge have already told you so?

An ammeter is a low-resistance device, while a voltmeter is high-resistance. In other words, NEVER connect an ammeter directly across the battery terminals. If you did, you would draw essentially infinite current across the short circuit and would blow up the battery, some of the circuits in your car, and/or ammeter, as well as perhaps starting a fire.

Remember, always measure current in series with, and voltage in parallel with, the circuit, or you'll destroy something!