Paul does make various allusions to the Book of Exodus, so it is also possible in this case. However, the context of Exodus 34:15 is different to that of 1 Corinthians 10:27 and the message is different. Any allusion to Exodus would have been for the purpose of correcting or redefining the restrictions imposed by the earlier text.
In Exodus, Moses is warned to destroy the altars and idols they find (34:13) because this could lead the Israelites to enter into a pact with the original inhabitants of the land, with the possible consequence that the Israelites will eat meat sacrificed to those gods, and marry among the foreigners.
In 1 Corinthians 10, Paul offers advice on avoiding being caught up in idolatry, but there is no incitement to violence against the heathens. In fact, 10:32 especially warns against giving offence, so a possible allusion to Exodus 34:13:
1 Corinthians 10:32 Give none offence, neither to the Jews, nor to the Gentiles, nor to the church of God
Exodus regards even unknowingly eating food sacrificed to heathen gods to be a sin, but Paul regards this as of no consequence. His meaning is caught in 10:23, where he contrasts the law on eating sacrificed meat with what is expedient or edifying:
All things are lawful for me, but all things are not expedient: all things are lawful for me, but all things edify not.
Paul says (10:20-21) he does not want the Corinthians participating at pagan feasts (the table of demons) - but this is different to being invited to a meal at which sacrificed meat may be served. He says there is no reason to avoid eating food that has been sacrificed to the gods, whether bought in the market (10:25) or at a meal to which you have been invited (10:27), unless you have been specifically told that it has been sacrificed (10:28), and the reason for this is that knowingly eating sacrificed meat sets a bad example for others. The line is drawn in 1 Corinthians 8:7-11:
1 Corinthians 8:7-11: Howbeit there is not in every man that knowledge: for some with conscience of the idol unto this hour eat it as a thing offered unto an idol; and their conscience being weak is defiled. But meat commendeth us not to God: for neither, if we eat, are we the better; neither, if we eat not, are we the worse. But take heed lest by any means this liberty of yours become a stumblingblock to them that are weak. For if any man see thee which hast knowledge sit at meat in the idol's temple, shall not the conscience of him which is weak be emboldened to eat those things which are offered to idols; And through thy knowledge shall the weak brother perish, for whom Christ died?
Clearly if you were in attendance at a sacrificial feast in a pagan temple, you would know that the meat was sacrificed to the gods, and verse 10:28 means you should not partake of the food. Verse 10:27 says to eat whatever has been set before you and therefore refers to an invitation to eat meat that you do not know to have been sacrificed: it is not an idolatrous feast.