The decision of accepting or not accepting your entry to Ukraine is made exclusively by frontier guard of Ukraine.
Notice of Ukrainian Embassy in RF clearly states that:
Решение на пропуск граждан Российской Федерации будут приниматься по
результатам контроля второй линии. В первую очередь внимание будет
обращаться на мужчин крепкого телосложения, следующих в Украину в
одиночку или в составе небольших групп.
Decision about admission of Russian citizens across the border will be
made considering the result of 2nd line control.
So what is the 2nd line control in practice? To learn that we should address Ukrainian Law № 1710-VI from 05.11.2009 "About border control". Paragraph 9 of this law concludes:
Procedure of 2nd line control is determined by the results of 1st line
This procedure can include:
- Determination of departure and destination points of the traveler, purpose of travel and the conditions of stay. Additional documents as
well as interview can be demanded if necessary.
- Determination of sufficiency of funds during the period of stay including return ticket or transit ticket to third-party country or
ability to receive additional funding legally on the
territory of Ukraine.
As one can see invitation fully complies to the first point of these requirements and can be claimed by the border officer.
So your entry (or rejection of entry) is completely up to you: your consciousness, self-confidence and behavior on the border, but nevertheless invitation letter is highly appreciated.