Depending on the type of plant, the inflorescence can be described by different terms. Phals have racemes. Some bulbos have umbels (think medusae). A good example of a classic spike inflorescence would be a spiranthes.
To answer simply, the plant is bearing an inflorescence would be correct, botanically
"In spike" is a horticultural term for something that doesn't matter much to a botanist (Yay! It's going to have flowers very soon!) , so there is no equivalent botanical term.
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It is correct that spike in a botanical sense refers to a specific type of inflorescence anatomy, as opposed to panicle, corymb, umbel, etc. In a horticultural sense, and the phrase "in spike" is pretty specifically horticultural, it is much more broadly applied, especially to monocots (like orchids) no matter what the anatomy of the inflorescence.