No, it will trim leading spaces but not all white space (e.g. carriage returns).
Edit
It seems you are looking for an UPDATE
query that will remove leading and trailing whitespace.
If by that you only mean "normal" spaces just use
UPDATE TableName
SET ColumnName = LTRIM(RTRIM(ColumnName ))
For all white space this should do it (from the comments here). Backup your data first!
UPDATE TableName
SET ColumnName =
SUBSTRING(
ColumnName,
PATINDEX('%[^ ' + char(09) + char(10) + char(13) + char(20) + ']%',
ColumnName),
LEN(ColumnName) - PATINDEX('%[^ ' + char(09) + char(10) + char(13) + char(20) + ']%'
, ColumnName) -
PATINDEX('%[^ ' + char(09) + char(10) + char(13) + char(20) + ']%',
REVERSE(ColumnName)) + 2)