No. Only if you actually instruct them to act for you and the do so. A one-off appointment - even if paid for - won't.
This isn't correct.
A solicitor cannot act for a party if there is a conflict of interest. A one-off appointment may very well be sufficient to give rise to a conflict of interest and in fact is likely to do so if it relates to the same matter.
It doesn't 100% follow that a single appointment will give rise to a conflict.
For example, if a person sees a solicitor for an appointment in which they only discuss the costs of instructing them and the standard procedure in a divorce and the person provides no detail of their situation and the person does not go on to instruct the solicitor, it is unlikely that there is anything that puts the solicitor in a conflict. Similarly if the person sees a solicitor about an completely unrelated matter, there may not be a confict.
If during the course of a one-off appointment, information is shared or advice given, there will be a conflict. For example, if a person tells the solicitor what their bottom line is or what they are willing to settle for - that puts the solicitor in a conflict situation and they could not act.
That said, it does happen that leading lawyers ( both solicitors and barristers) are often a target for people trying to conflict them out so in areas where this is an issue, they are wise to it and take steps to avoid it.