Although the word ‘conducive’ is still frequently used, I had not met with ‘conduce’ until reading a whimsical poem, The Poet and the Rose, by John Gay which starts with :-

I HATE the man who builds his name
On ruins of another's fame.

And concludes with this verse:

"Spare your comparisons," reply'd
An angry Rose, who grew beside;
"Of all mankind you should not flout us;
What can a Poet do without us!
In ev'ry love-song roses bloom;
We lend you color and perfume.
Does it to Chloe's charms conduce,
To found her praise on our abuse?
Must we, to flatter her, be made
To wither, envy, pine, and fade?"

I don't suppose the word is ever used today.

Con*duce, v. i. - [L. conducere to bring together, conduce, hire; con- + ducere to lead. See Duke and cf. Conduct, n., Cond.]
To lead or tend, esp. with reference to a favorable or desirable result; to contribute; -- usually followed by to or toward.

He was sensible how much such a union would conduce to the happiness of both. --Macaulay.

The reasons you allege do more conduce To the hot passion of distemper'd blood. --Shak.

Con*duce, v. t. - To conduct; to lead; to guide. [Obs.]

He was sent to conduce hither the princess. --Sir H. Wotton.