Sorry, but there's no actual credible evidence to suggest that.
If you're relying on Rupert Hughes' letter to Time magazine and a paragraph in his biography of Washington as your evidence, then you will fail. Please allow me to impeach your witness.
Hughes doesn't even get his facts straight. He basically refutes two things in his letter:
1) That Washington "converted to the Baptist creed" and,
2) That Washington was baptised by John Gano at Valley Forge.
Neither of these things have been asserted, however, in the recounting of Washington's baptism by Gano.
The story relates that Gano baptised Washington in the Potomac River, not at Valley Forge, which is a good hundred or so miles away. There's no need for Gano to have been at Valley Forge since that's not where he baptised Washington anywise.
But seriously, what are little things like "facts" to a historian, I guess?
Second, nobody claims that Washington converted and became a Baptist. In fact, quite the opposite. The relation of the story makes note of the fact that Gano baptised Washington despite his not converting. This, apparently, was in charactre for Gano, however. The baptism story itself relates "...the Rev. Mr. Gano transgressed the rule of his church by baptizing anyone who was outside the pale of his own denomination, but felt that he could not draw church lines too close to the Army, and so all were baptized by immersion who desired."
Hence, Hughes is attacking a straw man position, as well as simply not having his facts straight.
On December 13, 1799, Washington (aged 67 years) was exposed to a storm of sleet and developed a cold. He rested in bed at his home in Mount Vernon, Virginia.
On the morning of the 14th at 3:00, he had a severe attack of membranous croup. At daybreak, Mrs. Washington sent for the only physician, Dr. Craik. Two other physicians also came, but all three together could not save him. Washington died between 10:00 and 11:00 that night.
About four hours before Washington’s death, Father Leonard Neale, a Jesuit priest was called to Mount Vernon from St. Mary’s Mission across the Piscataway River. Washington had been an Episcopalian, but was baptized into the Roman Catholic Church that night. After Washington’s death, a picture of the Blessed Virgin Mary and one of St. John were found among the effects on an inventory of articles at his home
George Washington had an interest in Roman Catholicism for many years. His servant Juba stated that the General made the Sign of the Cross before meals. He may have learned this practice from his Catholic lieutenants, John Fitzgerald or Stephen Moylan. At Valley Forge, Washington had forbidden during “Pope’s Day,” the burning in effigy of the Roman Pontiff. As President, Washington slipped into a Catholic Church several times to attend Sunday Mass.
However, they do not provide any hard evidence on this site which is kind of a sensationalist antiMasonic site and I didn't really see any great convincing data on any others on a quick glance, so until we come up with some better information, we may simply have to disagree as to what really happened.