TL:DR: According to D&D-4e, yes they can... but there's no in-universe precedent for it.
This is mostly a deconstruction of your Wiki link. As, I have of yet to find, an instance where a cleric does so without theirs. I believe there was a point at which Crysania's prayers were unanswered, but that was from a lack of faith, not a misplaced necklace. I'm still looking for a part that says, "the Schwartz are in you!" - Skip to the last paragraph for the D&D rules.
What follows is an interpretation by one who has come to understand D&D, largely in part, through the epic saga that is Dragonlance. Beware the wall of text, offering no input on 'pre/post cataclysm'.
To start off, let's first look at another definition with the keywords, outward sign: (and a hint at the reasoning behind the lack of precedence for an answer)
This is a cleric's outward sign for their commitment and faith toward their god or goddess. [...] The Medallions also resist any effort to be removed by force from the cleric. It usually results in a severely shocked or burned hand. –Medallion of Faith, dragonlancenexus.com
Medallion of Faith –List of Dragonlance artifacts –Wiki:
(They "provide an outlet to channel power from". It does not say 'provides a means from which clerics cast spells'.)
Medallions of faith are worn by the members of the clergy of the true gods of Krynn, with the exception of the three gods of magic. These medallions are worn to serve two purposes; one is to proclaim the faith of the wearer, and, in the case of clerics, to provide an outlet to channel power from. Medallions of faith can be worn by the common citizenry, but they do not gain clerical power from the medal. The medallions are magical. The Medallions have a symbol of the god upon them. Medallions are used in conjunction with robes and vestments to display the nature and deity of the cleric.
Let's take a closer look:
can be worn by the common citizenry, but they do not gain clerical power from the medal.
With that wording, one might assume that the faithful do gain clerical powers, however:
Medallions are used in conjunction with robes and vestments to display the nature and deity of the cleric.
Channeling the power of a god requires faith above all else (and according to 'the rules', they need no such implement). No true cleric of Krynn requires magic to cast cleric spells:
The medallions are magical.
You might think that 'clerics don't require magic' requires a cite, so I'll let Raist handle that: (if you've a problem with 'requires faith above all else', ask your local theologian about it, as I am ill-prepared to defend that part)
Raistlin Majere: She's channeling the power of a god, you dolt. I'm wresting arcane energies from the very fabric of the universe - it's completely different. –IMDB
Editorial: (including a non-definitive example of a cleric without one, and AFAIK the only time this occurs)
Rephrase:
Can a 'priest' in Krynn personally cast cleric spells without ever having Been Given a Medallion of Faith?
IMO, absolutely not. No self-respecting god would forget to bestow their symbol of faith before granting that power. You might find cites to the contrary, but they would be far from the norm.
I'd surmise, that it's going to be difficult to find a passage, in which a cleric without their medallion is not also experiencing a lapse of faith. For, in but the one example I've found, I sincerely doubt that when "Crysania gave her Medallion of Faith to Palin to get past the grove"*, Paladine deserted her even momentarily.
Such earthly trinkets have no effect on the prerogative of someone who's literally been through hell and back. Someone of less faith however, might feel the need for such a bauble, and probably performs poorly without one.
Lack of precedence:
Lastly, this situation simply doesn't happen unwillingly:
Brigands attacked them, and when one of them named Steeltoe attempted to remove her Medallion of Faith, it harmed him.*
Yours is a valid question, but exactly why it isn't around their neck is integral to the answer. Tantamount to sacrilege, no person of continuing faith is ever without theirs, willingly - without a reason in good faith.
Permit me one last bit of speculation, that the prayers of those who have willingly discarded their medallion, surely go unanswered. If you are worthy, it is around your neck - there is no nominal precedent for one without the other.
Unfortunately, the one cleric who would be most apt to ignore this rule if it does exist, is also one and the same as our only example: Crysania. So, in lieu of emailing the authors, we can but look up the rules.
*: Crysania Tarinius, dragonlancenexus.com
D&D rules:
Which cleric powers are usable without a Holy Symbol? –RPG.SE, paraphrased:
Clerics can use (almost) all of their powers when disarmed and without implements. With which, you would simply get a bonus (in D&D-4e).
