Can the campaign mode for Star Wars: Imperial Assault be played if one player is not always able to attend?
Short answer: 

It shouldn't be a problem as long as you guys are willing to share control of that player's character when he isn't available or are OK with taking some risk with game balance by having the number of players vary between missions.

Detailed answer:

The number of players in the game does matter and is meant to be fixed. The campaign setup (Rules Reference Guide, Page 7) requires that each player choose a Hero and handles assignment of the Legendary/Heroic cards for games with less than 4 players at campaign start time. If the number of players changes, you'll need to add/remove Legendary/Heroic cards as appropriate.

Campaign setup also affects the building of the side mission deck (Rules Reference Guide, Page 17) as each hero's red Side Mission card will be inserted into the deck.

Critically, the number of credits granted at the end of each session scales based on the number of players. The game wasn't designed for this to vary.

You likely could change the number of players between missions, temporarily removing their side quest and granting less credits at the end, but this means that the pool of players will have less credits than they ordinarily would have had. This can be fairly impactful, as it's a common practice to pool resources to load up one or two heroes with great end-game weapons and attachments. Additionally, the missing hero would either need to be granted XP upon rejoining the game or fall behind.

There are also some logistics to consider: if you have the missing player's hero controlled by the group, you may want to coordinate which abilities they would want to pick if you're doing more than one mission at a time.

I personally feel it's best to just control that player's character in their absence to keep the number of players constant. Some groups will opt to always play with four heroes, even if there are less players, as some missions feel more balanced with a full group and support characters get a greater chance to shine.