Yes. Fukuoka's official visitor guidance explicitly says going to a yatai alone is fine. You need one counter seat and an order, not a Japanese friend to bring you in. At a tiny food stall, a party of one is a practical size. Fukuoka City's yatai guide
The awkward part tends to happen before you sit down: people are already talking, the stools look close together and you cannot tell whether that gap is available. Give the staff a simple question rather than trying to work it out from the pavement.
ひとり、入れますか？ — Hitori, hairemasu ka? — “Is there room for one?”
If there is a queue, join it. An empty-looking stool is not permission to pass the people waiting.
Choose dinner before choosing a famous name
Open the official yatai map and select a small area you can comfortably reach from your hotel. Pick two stalls whose menus interest you, so a closure or a long queue does not end the evening.
Ramen is one possibility. The city's yatai directory also describes oden, gyoza, grilled skewers and tempura. If you want to watch food being cooked and try a second place, a small dish first leaves room. If what you want is a bowl of noodles and bed, that is a perfectly coherent plan too.
Read the prices before sitting. When you cannot identify a dish, point to it and ask これは何ですか？ (Kore wa nan desu ka?, “What is this?”). A translation app is useful for a menu; an elaborate introduction is unnecessary.
A first order you can actually use
The city recommends at least one drink and one dish per person. A drink does not have to mean alcohol: its guide lists options including tea and soft drinks. Carry yen in cash, because cashless payment is not available at every stall.
For a recommendation, ask おすすめは？ (Osusume wa?). Then check the menu price of what is suggested before ordering. This is particularly useful if you cannot tell whether a displayed price is for one skewer or a serving.
Keep your bag close and small. The counter is shared space, and a suitcase gives the cook a problem you can solve beforehand by leaving it at your hotel. Yatai do not have their own toilets; ask staff where to go if needed. These are the city's practical points, not a requirement to master restaurant etiquette before dinner. Visitor guidance
You can join a conversation if one opens up. You can also eat while watching the cooking. Close seating creates an opportunity to talk; it does not guarantee English conversation or oblige the person beside you to entertain you.
When finished, お会計お願いします (Okaikei onegaishimasu) asks for the bill. If others are waiting, move on after paying rather than treating the seat as your base for the whole night.
Leave room for a closed stall
Yatai have individual schedules, and weather can stop them opening. The city's general guide puts most openings around 6:30–7 PM, with many closing around midnight; that is background for planning, not the opening promise of a specific stall.
If your first choice is closed, use the second one you saved. For a first solo visit, an open stall with food you want is more useful than spending the night searching for a name from an old video.