Yes, it is possible to disable the trigger, but keep in mind that you are disabling that trigger for everyone using the table, not just for what the trigger is doing. I don't know of any way to allow a trigger to function for some users/spids and not for others, except to include code within the trigger to make it decide that it shouldn't run under some conditions.
If SQL Server 2000 and one can alter the trigger then one can use SET CONTEXT_INFO in SP and then check master..sysprocesses from trigger.
Might also insert DBCC INPUTBUFFER(@@SPID) results into temporary table in trigger to check for proc name in EventInfo column. Would work in SQL Server 7 and would not require any additional code in SP, but would hurt trigger performance, be kludgy, and require hard-coding proc name(s) in trigger.