Air taxi Captain reported receiving a low altitude alert from BWI Tower when the FMS failed to sequence properly following a rushed departure.

Narrative

Departing 33R CONLE5 RNAV DEP SCOOB Transition 5. Due to a temporary ground stop that morning in BWI Ground Control gave us the option to wait at the ramp or taxi via Q and hold short of runway 33R. We elected to taxi via Q and hold short of 33R until the ground stop was lifted. During the taxi to 33R we noticed a long line of aircraft holding short of runway 28 for departure and they were advising BWI Tower that they were shutting down their engines to save fuel because of the ground stop. Upon reaching the end of Q taxiway and holding short of 33R and monitoring tower frequency 119.4; after a few minutes Tower mentioned the ground stop had been lifted and advised waiting aircraft to start their engines; if necessary. I instructed the PM to contact Tower and that we were ready to depart. Tower requested if we could do a priority take off with no delay; I instructed the PM that we could accept that request. Tower instructed us 'Cleared to take off runway 33R RNAV to SUGGS'. I immediately called for the 'Runway Line up Checklist' and taxied on to 33R for departure and checked that NAV Mode was selected for the RNAV departure. Tower notified us again that we were a priority departure and no delay; and we advised them that we were on the roll on 33R. After departing 33R and above 644' AGL the Flight Director did not sequence & capture the left turn to SUGGS intersection. (The CONLE5 RNAV departure from 33 L & R requires a climbing left 180 degrees turn in the opposite direction to SUGGS intersection at or below 7000.) I immediately turned off NAV mode and went to HDG (heading) mode and initiated a left turn to SUGGS and was hand flying to go direct. Once the course was corrected; I then initiated a climb to cross SUGGS at or below 7000. During the turn to SUGGS intersection received an altitude alert from Tower and advised Tower we were climbing and going direct SUGGS intersection. Tower instructed us to contact Potomac Departure; upon contacting Potomac Departure they advised us to continue climbing on the CONLE5 RNAV Departure; the rest of the flight continued uneventfully to our destination.Even though as PF; I had reviewed the CONLE 5 RNAV departure with the PM on the ramp after engine start; I should have been more cognizant of the fact that the NAV MODE might not sequence or capture such an excessive turn to on the initial departure and that we should fly initially in HDG Mode until we are direct SUGGS intersection and then select NAV MODE.I had leveled off during the climb once I determined our flight director was not giving us the correct guidance causing the altitude alert. In hindsight; I should have continued to climb but once I had established the correct course I immediately started climbing. In addition; I should have refused the priority takeoff; giving me another opportunity to review the departure prior to taking off on RWY 33R.