I remember hearing that sometime in WW2 that the UK Prime Minister Winston Churchill made an offer to Irish Taoiseach (= Prime Minister) Éamon de Valera that the UK would give Northern Ireland to Ireland in exchange for Ireland joining the war on the allies side. And that de Valera turned it down, because of fears that the large Protestant population there would reduce the electoral chances of his own FF party.
Is this true? (a) Did Chuchill offer Dev the North? (b) Did he turn it down for electoral reasons?
This is true but disingenuous. De Valera rejected the offer because he knew it wasn't Churchill's offer to make: as Prime Minister Churchill couldn't unilaterally kick Northern Ireland out of the UK against the (dominant) wishes of the Unionist community in Northern Ireland. It was reasonable to expect that the wartime offer would be withdrawn in peacetime due to the Protestants of Northern Ireland's overwhelming rejection of joining Ireland and the dominance of Protestants in 1940s Northern Ireland.
Did he turn it down for electoral reasons?
I'm not sure what you are asking here. Was Dev reluctant to bring in NI? Hardly - Dev ran for the NI elections as Sinn Féin member in the 1921 NI elections after the [Westminster] Government of Ireland Act had partitioned the country.
He walked out of the Dáil Éireann chamber in protest at the passage of the Treaty in 1922 and was involved in the Irish Civil War hoping to bring about a Republican United Ireland. Having failed he entered the Dáil with Fianna Fáil in 1927 but in 1933 he again ran for election in NI and was elected to Stormont for the constituency of South Down. He held the seat until 1938 but refused to actually take his seat at Stormont as he was making the point that South Down belonged to Dáil Éireann in a united Ireland.