Householder Konrad, interested,
Going for refuge, seeking refuge under the Tripple Gems - without such any long lasting success:
No, not really, only Paccecabuddhas would be able to practice the Noble-Path without refuge. Just think on how many livetimes the Bodhisatta hardly tried, and how good he tried in relation to western/modern people today, who think such might be possible, easier. At times the Dhamma of the Buddha is still vitally alive by the Sangha of the Buddhas good following monk, even such a person, having such potency or having reached the path, as well as those who had won the path in previous existance, would seek out for the refuge under the Tripple Gems, eventually join the Sangha also outwardly.
Some issues on that matter on faulty refuge or no have been answered here: How does one become a lay Buddhist?.
Today there are many how think "love and marriage" can be seperated, seeking after avoiding certain duties that come from relationship and also hold on greedy on old habits, views and relations, but all those popular approaches, often hardly neglecting monasticism and renounced life, would, how much what ever thought practiced, not equal only taking refuge into the Buddha, his good Dhamma and his straight following disciples on the road of homelessness.
So again in short to the two questions:
Can a person follow the Buddha's teachings without taking refuge?
Generally no. Only a very seldom Paccecabuddha-canditate could, and he would not having get known our current Buddha, Dhamma, Sangha.
Can someone attain enlightment without taking refuge?
Again: Generally no. Only a very seldom Paccecabuddha-canditate could, and he would not having get known our current Buddha, Dhamma, Sangha.
So good to hurry, seek out and nourish inwardly and outwardly the Tripple Gems and ones relation tendency because not even difficult to trace this days but also fast disappearing for the most. No more tracing is already a sign for one to possible have lost the track of Upanissaya (strong condition), which relays on paccaya (causes given) from ones past and present actions by thoughts, words and deeds.
Hurry up if feeling, seeing, seriousness would bring great long term happiness and beyond.
(Note that this gift of Dhamma is not dedicated for trade, exchange, stacks or entertainment but as a means to make merits toward release from this wheel)