I would say that the concept of carpe diem is a central theme of Marlowe's "The Passionate Shepherd to His Love." However, I'd note that we could find additional degrees of nuance and criticism were we were to introduce a second poem—Sir William Raleigh's "The Nymph's Reply to the Shepherd"—into this analysis.
In this second poem, we see the Shepherd rejected on the grounds that his vision of love is naive, and cannot hold up to the ravages of time. As the Nymph says:
The flowers do fade, and wanton fields,
To wayward winter reckoning yields,
A honey tongue, a heart of gall,
Is fancy's spring, but sorrow's fall.
Thy gowns, thy shoes, thy bed of Roses
Thy cap, thy kirtle, and thy poises
Soon break, soon wither, soon forgotten:
In folly ripe, in reason rotten. ("The Nymph's Reply to the Shepherd")
Again, do be aware that Raleigh's poem is distinct from Marlowe's; but, in its response to Marlowe, it does provide interesting commentary on Marlowe's original work, and this commentary is deeply relevant to your particular question here. Raleigh's response reveals the degree to which the Shepherd's original entreaty is short-sighted and unsustainable (which is proven, at least in Raleigh's work, when he is rejected by the Nymph).