Yes, the manpower will be reinforced but the equipment won't.
The effect of this is that the stats gained from the equipment are reduced proportionally to the amount of equipment - so, for example, if a division with only 10 infantry brigades and 0 support companies has only 50% of the required equipment, it would (or should) have exactly the same stats as a fully-equipped division made up of 5 infantry brigades and 0 support companies.
If a division is down on manpower, all stats are lowered, including speed* - though I can't say I've ever checked if a division with 50% manpower and 50% equipment would fight at 25% stats or 50% stats.
*This, as far as I can tell, only applies to divisions faster than 4km/h. Don't quote me on this.