No... the A service includes a lot of things........
I can get my manual and list the included items.

Ok, for all 2001 models (US), an A - service includes:

Interior
FUNCTION CHECK
Check Tele Aid function
Warning indicator lamps, horn
Headlamps and exterior lamps
Windhield/headlamp,
wiper and waster systems
Check seat belts for damage
Reset FSS counter
Heating & ventilation: replace dust filter.


Wheels
Correct tire pressure


Engine Compartment
Engine oil and filter change

CHECK AND CORRECT FLUID LEVEL
Engine coolant/antifreeze protection
Brake system
Windshield/headlamp washing system
Lubricating engine hood (Models 129, 170, 208, 210)
Inspect hood latch and safety latch for proper operation (Models 203, 215, 220)

Trunk
Check and correct tire pressure (spare) (Except Model 170)

__________________
2006 E350 w/ 155k miles (Daily Driver)

Previous:
1993 300E 3.2L Sedan w/ close to about 300k miles
2003 E500 Brilliant Silver (Had 217k miles when totalled!)
1989 300E with 289,000 miles (had for <1 yr while in HI)
03 CLK 500 cabrio (Mom's)
2006 C230k (Dad's)
1999 S420 (Mom's/Dad's)
2000 C230k Sport sedans
2001 CLK320 Cabrio (Mom's)
1995 C280 My First Mercedes-Benz... (155k miles. EXCEPTIONAL AUTOMOBILE. Was Very hard to let go of!)