Does the quantity (magnitude) of sins of an individual affect the time to awake kundalini for a beginner?
In Yoga, raising the Kundalini depends solely on Yogic practice. So, if one does as prescribed, he/she will meet success. So, the question of accumulated sins don't really come into the picture and it is not an obstacle. Yogic practices are there to clear the sins
However, whether a person, whose sins are on the higher side, will be attracted towards Yogic practice is another question and probably the answer to it is NO.
From Hatha Yoga Pradipika:
Yena mārghena ghantavyam brahmasthānam nirāmayam
Mukhenāchchādya tadvāram prasuptā parameśvarī ||
The Parameśwarî (Kundalinî) sleeps, covering the hole of the passage by which one can go to the seat of Brahma which is free from pains.
Kundalî Sakti sleeps on the bulb, for the purpose of giving moksa to Yogîs and bondage to the ignorant. He who knows it, knows Yoga.
Kundalī kutilākārā sarpavatparikīrtitā
Sā śaktiśchālitā yena sa mukto nātra samśayah ||
Kundalî is of a bent shape, and has been described to be like a serpent. He who has moved that Śakti is no doubt mukta (released from bondage)
Youngster Tapaswini (a sheascetic), lying between the Ganges and the Yamunâ, (Idâ and Pingalâ) should be caught hold of by force, to get the highest position.
Idâ is called goddess Ganges, Pingalâ goddess Yamunâ. In the middle of the Idâ and the Pingalâ is the infant widow, Kundalî.
This sleeping sheserpent should be awakened by catching hold of her tail. By the force of Hatha, the Śakti leaves her sleep, and starts upwards.
This sheserpent is situated in mûlâdhâr. She should be caught and moved daily, morning and evening, for ½ a prahar (½ hours), by filling with air through Pingalâ by the Paridhana method.
Now, see the procedure for raising/awakning of the Kundali Shakti:
sati vajrāsane pādau karābhyām dhārayeddrdham
Ghulphadeśasamīpe cha kandam tatra prapīdayet ||
Keeping the feet in Vajraâsana (Padmaâsana), hold them firmly with the hands. The position of the bulb then will be near the ankle joint, where it should be pressed.
Vajrāsane sthito yogī chālayitvā cha kundalīm
Kuryādanantaram bhastrām kundalīmāśu bodhayet ||
The Yogî, sitting with Vajraâsana and having moved Kundalî, should perform Bhastrikâ to awaken the Kundalî soon
There are other methods too, like performing Bandha and Pranayam etc, which are capable of raising the Kundalini.
So, in short, it depends on whether the prescribed practices are performed correctly and mastered by the aspirants and not on whether the aspirant has lots of sins.
Brahmacharyaratasyaiva nityam hitamitāśinah
Mandalāddrśyate siddhih kundalyabhyāsayoghinah ||
Only one who delights in the life of celibate (brahmacharin), and always conforms to a moderate and salutary diet, and who practices Yoga in the form of stimulating Kundalini approaches Siddhi within forty days
This suggests that ANYONE can achieve the said Siddhi in the stipulated time of 40 days, given that he/she has performed the necessary practices and irrespective of how much sin he/she might have accumulated.
However, another point is that the scriptures also say that too much of accumulated sins will cause delay in getting the Guru. And, without the Guru one may not achieve success particularly in Yoga.
I think that the Vayaviya Samhita of the Shiva-PurAna throws light regarding this:
guror Aloka-mAtrena sparshAd sambhAshanAd api| sadhyah samjnA bhaved jantoh pAshopakshayakArini|| meaning : By the very glance and touch or speech of the Guru, a disciple gets pure knowledge that destroys his bondages[sins].
yathA prajjvalito vahnir sushka-kAstham cha nirdahet| tAthAyam api santushto guruh oApam dahet kshanAd||
meaning that as the burning fire devours the dried wood, the Guru being pleased can burn all sins in a moment.(Ref:DikshA-sAra, Amita, Mahamilan Math, page 28).
So grace of an able guru is what is important.
The Kularnava-Tantra says
mantridoshom cha rAjAnam jaAyAdoshah patim yathA| tathA prApnoti asandeham shishya-pApam gurum priye|| meaning :[ Lord Shiva is telling PArvati] My beloved! As the sin of kings is taken by tuhe king and of wife by the husband, the Guru takes tye sin of the disciple.(Ibid page 67),. Here also, the Guru relieves the disciple of the sin.
YogavAsitha (sarga 12 )says
ardham sajjana-samparkAd avidyAyA vinashyati|chaturbhagas tu sAstrArthair chaturbhagah svayatnatah|| (Ibid, page 37) meaning : half of the avidya (sin) is destroyed by company of the saints, one fourth by reading shAstras and one fourth by one's own spiritual practice.
Finally the Gautamiya-Tantra says
mulapadme kundalini yAvad nidrAyita prabho/tAvad kinchid na sidhyeta mantra-tantra-archanAdikam// jAgarti sA yadA devi bahuvih punya-sanchayAh/tadA praAdam AyAti mantra-tantrarchanAdayah// meaning: so long as the Kundalini is sleeping at tye mukAdhAra, the chanting of mantra, practice of tantra or worship---none bear any fruit. When She is awakened by accumulation of many virtues (puNya), then all these practices become pleasant ones.
To conclude, unless many virtues are accumulated, the Kundalini can not be awakened. Getting an an able Guru is the result of accumulation of a huge amount of puNya and so this means that the person have reduced a major part of his sins already.