As Dottard already mentioned, the text does not say explicity, but I think, to answer the question, the implications offer a resounding "no", despite his petition to the LORD.
First, recall that when Balaam met the Angel of the LORD on the road, the Angel met him with sword drawn and said "I have come here to oppose you because your path is a reckless one before me". The text tells us that the LORD was wroth with Balaam, and sent His Angel to resist, perhaps even to slay, him.
Let us then remember it was merely a petition to God from Balaam, not a promise from God to Balaam.
Third, Numbers 31 begins with the LORD commanding Moses to take vengeance upon the Midianites for what they instigated against Israel at Baal Peor:
Numbers 31:1-2 (NIV),
1 The Lord said to Moses, 2 “Take vengeance on the Midianites for the Israelites..."
Balaam was slain during this vengeance, as it reads in Numbers 31:7-8 (NIV),
7 They fought against Midian, as the Lord commanded Moses, and killed every man. 8 Among their victims were Evi, Rekem, Zur, Hur and Reba—the five kings of Midian. They also killed Balaam son of Beor with the sword.
Balaam was not merely accidentally killed in the skirmish, but was targeted. How do we know?
When the Israelites who raided the Midianites came back with women and children alive from the battle, Moses, Eleazar, and the other leaders of the people were furious, and say the following:
Numbers 31:15-16 (NIV),
15 “Have you allowed all the women to live?” he asked them. 16 “They were the ones who followed Balaam’s advice and enticed the Israelites to be unfaithful to the Lord in the Peor incident, so that a plague struck the Lord’s people.
Baal Peor is perhaps the greatest stain on the history of the nation of Israel according to the Tanakh.
Not only do we have the record of the incident that took place there (Numbers 25:1-5), we also have the residual references afteward, including:
Deuteronomy 4:3 (NIV),
3 You saw with your own eyes what the Lord did at Baal Peor. The Lord your God destroyed from among you everyone who followed the Baal of Peor...
Psalm 106:28 (NIV),
28 They yoked themselves to the Baal of Peor and ate sacrifices offered to lifeless gods
Hosea 9:10 (NIV),
10 “When I found Israel, it was like finding grapes in the desert; when I saw your ancestors, it was like seeing the early fruit on the fig tree. But when they came to Baal Peor, they consecrated themselves to that shameful idol and became as vile as the thing they loved.
So, for the next nearly thousand plus years, Israel is still being reminded of the utter reproach they suffered at Baal Peor, because of how Balaam, (after his prayer in which he petitions for a righteous death, no less), cast a stumbling block before Israel.
In fact, Balaam is never regarded as righteous, but rather, in the Tanakh, always as a soothsayer, or someone who practiced divination, which eventually became a capital offense in Israel (1 Samuel 28:9).
In the New Covenant Scriptures, Balaam is called a prophet, but described as ""insane". In Revelation, the Lord Jesus brings up Balaam and castigates the church at Pergamum for following a teaching originally ascribed to him (See: Revelation 2:12-14).
It seems then to me, that the testimony against Balaam is secure. He was an unrighteous madman who got what he deserved.