Definitely.
In the past, teams have made the signing/trading for a captain a priority. 27 times in all.
Anaheim signed Scott Niedermayer for the sole purpose of being a captain, simply because he had the reputation around the league as a leader.
Scott Mellanby was brought to Atlanta spoecifically to be the captain.
Calgary signed Bob Boughner strictly for his leadership skills and named him as co-captain
Brendan Shanahan, with no captain experience was signed by Hartford with the intent of being the captain
Chicago signed Martin Lapointe to be captain, they signed Doug Gilmour to be captain, Terry Ruskowski was made captain his first day in Chicago
Columbus made Adam Foote captain right away
Dallas took Paul Shmyr in the 1979 expansion draft to be their captain. In 1970 they signed Ted Harris away from Montreal to be their captain.
Detroit obtained Ted Green from Minnesota and instantly named him captain. In 1975 Detroit signed Terry Harper with the intention of naming him captain.
Montreal named Pierre Turgeon captain the day he arrived off the plane
Lanny McDonald was named captain of Kansas City/Colorado/New Jersey the day he arrived
The Islanders made Trevor Linden the captain the minute he arrived. The Islanders also signed Mike Peca with the purpose of naming him captain.
Twice, the New York Rangers have obtained Mark Messier and named him an instant captain. Phil Esposito was an instant Ranger captain upon his trade from Boston
Winnipeg made Troy Murray captain the day he joined the team.
Pittsburgh obtained Orest Kindrachuk with the intent of making him captain
St. Louis signed Scott Stevens with the intent of making him captain.
San Jose obtained Bob Errey with the intent of making him captain. Todd Gill was made an instant captain (this one makes me laugh)
Tampa Bay made Mikael Renberg captain the minute they obtained him.
Toronto made Robber Ramage captain the minute he became a Maple Leaf
Vancouver made Mark Messier the captain the minute he signed
Washington made Rod Langway an instant captain.
Note: Dave Andreychuk's first year in Tampa was 2001-02, Tampa did not file any official captain's with the league that year.