I'll go ahead and apologize for what is very clearly overanswering your question Nimlothiel :/. I'm just doing this so that others less familiar gain an understanding of the common past tense Neo-Sindarin conjugations. The short answer to your question is: yes. The long answer is as follows:
One theory -and it's the one I use because I always like looking back in the fictional past - is to look back at what a likely conjugation of a primitive elvish root may be, then trace it forwards to Sindarin. The conjugation of primitive elvish verbs you see here is likely (note I say 'likely', this is most certainly not attested 100% good scholarly Sindarin, it's in the world of Neo-Sindarin) something that would occur after the split of the Sindar from the rest of the Teleri as Thingol goes off into the forest because the birds are chirping his song. I say this because it encorporates parts of what we see as the Quenya past tense and Quenya perfect tense: Sindarin's past tense encorporates both shades of meaning, to say "I have eaten" and "I ate" would be the same thing.
For I-Stems, the past tense would be formed in two ways depending on the ending. If the Sindarin verb ends in -b, -d-, or -g (which would be a primitive -p, -t, or -k), take the primitive root and prefix the stem vowel (unless if there's a primitive prefix like in Echad's historical case of etkat from et-kat), then nasal infix '-ne' to the end of the verb. Mad- 'to eat', prim. Mat -> a-mat-ne -> amatne -> amante -> *avant 'He/She/It ate'. For pronoun suffixes make the root intervocalic, re-add the '-e' that was dropped, then add the suffix: Thus *avannen = "I ate". If the root did not end in the above stops: lengthen the pre-existing stem vowel instead of suffixing '-ne'.
This is where things get a little foggier: you'd expect to see '-ne', but according to Car's past tense singular of agoren we're left to wonder where the '-e-' came from in the phonological development from primitive elvish; perhaps it was through analogy with the other words that ended in e's that were lost in the third person singular but went on to appear to "regain" the vowel when it gained pronoun endings. Aldaleon, as seen above, neatly avoided this issue by providing a doubled translation. He's more experienced so please: take the past with a grain of salt.
So we'd expect from the verb Cen to do one of the following two things: Primitive Ken -> e-ken-ne -> ekénne -> *egín. Or, rather, if somehow it gained by analogy - or some other weird happenstance - a 't', it might look like Ken -> e-ken-ne -> ekenne -> egenn -> egent. This leads us to the headache of a game of figuring out the pronoun suffix accepting forms (first person singular used for example)! With the first choice we could get *egínen or perhaps *egínnen, the second choice leads us to *egennen. Ironically after this search, "I have not seen" which one's more correct.
Edit: Please see below: Elaran's more experienced than me so please take his word for it!