The unit was a regular pre-war engineering unit. It was a motorized engineering unit and attached to General Headquarters. The first reference I can find on the unit is from the France 1940 campaign. The unit was attached to Guiderian's XIX Panzer Korps. It supported the flank of the Korps as they crossed the Muese. One company helped the 1st Panzer Division to clear the village of Chemery (Chehery). It then helped repulse a counter attack of French armour destroying several tanks with shaped charges and flamethrowers. The 43rd's commander was killed in this action. For the rest of the campaign it supported the Korps Flank along with 37th Anti-tank Bn. (of 1st Pz) and 4th Panzer Reconnaissance Bn. These references are from "Gudarian's XIX Panzer Korps in France" and the Signal/Squadron book on the GrossDeutschland Inf. Div.
The next reference to the unit finds them in the Soviet Union in the summer of 1941. 2nd company of the unit was drawn from 3rd Panzer Group to help 7th Panzer Division and 20th Motorized Infantry to cross the Dvina River near Ulla. The action was part of the German Armies advance on Vitebsk and Smolinsk. This reference comes from the U.S. Army's "Small unit tactics on the Russian Front" series. Go to River to read a summery of the account.
On April 1, 1942 the Großdeutschland Infantry Reg. was enlarged to a Motorized Infantry Div. 43rd St. Pioniers became Pionier Bn. Großdeutschland. Thanks to Marsh Wise for this information.