It could happen, yes. There's no real evidence that the Pythia's responses were designed for the self-interest of the Oracle, as was often assumed in mid-20th-century-and-earlier scholarship. But there are three stories on record of the Pythia being influenced by specific parties.
Two, recorded in Herodotos 6.66 and Thucydides 5.16, are of how Athenians influenced the Pythia to give particular responses to the Spartans. In Herodotos' story, after the corruption was discovered, the Pythian priestess was removed from office and a prominent Delphian citizen who aided the Athenians was exiled. A third story, in Herodotos 5.90 and 6.123, is of the Alkmaionids bribing the Pythia in the 6th century BCE. That one is early enough that we can't be confident of the details of the story. None of the three stories can be corroborated.
Later evidence shows that corruption continued to be feared. Here's one official report of an Athenian state consultation of the Oracle on what they ought to do with part of the sacred land owned by the cult of Demeter and Kore at Eleusis. This report dates to 352/1 BCE and is recorded in Inscriptiones graecae II^2 204 (oracle 262 ed. Parke-Wormell, H21 ed. Fontenrose; I quote the translation by Hugh Bowden, Classical Athens and the Delphic Oracle [2005] pp. 88-90):
[It is decreed] that the Secretary of the Council (Boulē) write on two sheets of tin, equal and alike, on the one:
if it is more profitable and better for the people of Athens that the Basileus lease out the parts of the Sacred Orgas now under cultivation, the parts outside the boundaries, to pay for the building of the portico and the repair of the sanctuary of the Two Goddesses;
on the other sheet of tin:
if it is more profitable and better for the people of Athens that the parts of the Sacred Orgas now under cultivation, the parts outside the boundaries, be left untilled for the Two Goddesses.
As soon as the secretary has written on it, the President of the Proedroi [the nine men overseeing the conduct of the Assembly that day] shall take each sheet of tin and wrap it up; having wrapped each in wool, he shall put them into a bronze jug in view of the People; the Prytaneis [the fifty councillors currently responsible for the day-to-day administration of political business] shall prepare these things, and the Treasurers of the Goddess [Athena] shall bring forward a gold and a silver jug right away to the people, and the president, having shaken the bronze jug, shall take out the sheets of tin each in turn and put the first one into the golden jug and the second into the silver jug and close them up, and the President of the Prytaneis shall seal them with the public seal, and whoever of the other Athenians wishes shall add their seal; as soon as they have been sealed, the Treasurers shall carry the jugs to the acropolis; the people shall choose three men, one from the Council and two from all Athenians, who will go to Delphi and ask the God which of the inscriptions the Athenians should act in accordance with concerning the Sacred Orgas, the one from the gold jug or the one from the silver...
These elaborate procedures for ensuring that no mortal had access to the contents of the jars nicely illustrates the fear of corruption.