Saying that Hitler joined the Nazi party as a spy would be an extreme simplification but I can see where the basis of it comes from.

Hitler joined the new born party, as party member 555, after a party meeting in September 1919 with the approval of his military superior CAPT Karl Mayr.

CAPT Mayr was a Staff Officer on the staff of General von Mohl. CAPT Mayr was training and controlling a body of agitators to counter the activities of propagandists for Communist and Independent Socialist revolutionaries who were active in the transit camps that all demobilising personnel had to pass through. The first training course was held 6-12 June 1919 at Munich University.

Hitler had been temporarily blinded in a gas attack in October 1918 and spent the last month of the war, and it's immediate aftermath, hospitalised in Stettin. By June 1919 he had been released from hospital and was serving in the Command Company of the Second Bavarian Infantry Regiment and attended the agitator's course conducted by CAPT Mayr. On 22 July 1912 Hitler was sent, as part of a "propaganda commando" under a SGT Beyschlag, to the large demobilisation camp at Lechfeld, for which he was commended as an orator and propagandist. After this CAPT Mayr began to use him on his own both as a propagandist and as a political agent and adviser on the various right wing political groups in Munich. It was as part of these duties that Hitler joined the young Nazi party.

So Hitler joined the Nazi party as an anti communist and anti Independant Socialist political agent serving in the army. It would be awkward to call him a "spy" with it's implications of secrecy. He didn't keep his connection to the military secret, he used it. The party probably obtained money from the army through him, and certainly by seconding soldiers to the party's activities.

Sources: The Mein Kampf english translation by Ralph Manheim, in particular, the introduction by D.C. Watt, and Chapter 8.